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A

MAZE

IN

ZAZAZA ENTER AZAZAZ

AZAZAZAZAZAZAZZAZAZAZAZAZAZA

ZAZAZAZAZAZAZAZAZAAZAZAZAZAZAZAZAZAZ

THE

MAGICALALPHABET

ABCDEFGHIJKLMNOPQRSTUVWXYZZYXWVUTSRQPONMLKJIHGFEDCBA

12345678910111213141516171819202122232425262625242322212019181716151413121110987654321

 

 

A

HISTORY OF GOD

Karen Armstrong 1993

The God of the Mystics

Page 250

"Perhaps the most famous of the early Jewish mystical texts is the fifth century Sefer Yezirah (The Book of Creation). There is no attempt to describe the creative process realistically; the account is unashamedly symbolic and shows God creating the world by means of language as though he were writing a book. But language has been entirely transformed and the message of creation is no longer clear. Each letter of the Hebrew alphabet is given a numerical value; by combining the letters with the sacred numbers, rearranging them in endless configurations, the mystic weaned his mind away from the normal connotations of words."

 

 

THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY

THE ACCOUNT IS SYMBOLIC AND SHOWS GOD CREATING THE WORLD BY MEANS OF LANGUAGE

AS THOUGH WRITING A BOOK BUT LANGUAGE ENTIRELY TRANSFORMED

THE MESSAGE OF CREATION IS CLEAR EACH LETTER OF

THE

ALPHABET

IS

GIVEN

A

NUMERICAL

VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS

REARRANGING THEM IN ENDLESS CONFIGURATIONS

THE MYSTIC WEANED THE MIND AWAY FROM THE NORMAL CONNOTATIONS OF WORDS

 

 

THE MAN WHO LOVED ONLY NUMBERS

Paul Hoffman

1

999

Page 217

"Mathematicians in India in the sixth century had developed a place value system and introduced the concept of a zero to keep their symbols in their proper places. Thus a 1 with an 0 after it, or 10, is a very different number from a 1 alone. Erdos, who always joked that he was old and stupid, said the Indians were very clever, not just in their discovery of zero, but in their choice of similar- sounding Hindi words for stupid person (buddhu) and old person (buddha).

In the seventh century, Hindu scholars introduced Islam to the Indian number scene, and the ideas of zero / Page 216 ( omitted) and place value spread rapidly throughout the Arabic world. Six centuries later, Fibonacci was so impressed with the ease of the Hindu-Arabic numerals that he wanted to make Pisan merchants aware of them. In 1202, he wrote Liber abaci (Book of the Abacus), which, despite the title had little to do with the Abacus and a lot to do with liberating computations from the yoke of Roman numerals. The book seems quaint from the vantage point of the twentieth century, because it explains what we take for granted.

"The nine Indian figures are: 9 8 7 6 5 4 3 2 1 , and with the sign Zero. . . any number can be written."

 

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

2
IS
28
10
1
9
UNIVERSAL
121
40
4
4
MIND
40
22
4
3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
33
First Total
378
162
27
3+3
Add to Reduce
3+7+8
1+6+2
2+7
6
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
6
Essence of Number
9
9
9

 

 

9
UNIVERSAL
121
40
4
4
MIND
40
22
4
2
IS
28
10
1
3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
33
First Total
378
162
27
3+3
Add to Reduce
3+7+8
1+6+2
2+7
6
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
6
Essence of Number
9
9
9

 

 

E
=
5
-
2
EX
11
2
2
U
=
3
-
6
UMBRIS
82
28
1
E
=
5
-
2
ET
25
7
7
I
=
9
-
10
IMAGINIBUS
104
50
5
I
=
9
-
2
IN
23
14
5
V
=
4
-
9
VERITATEM
113
41
5
-
-
35
-
31
First Total
358
142
25
-
-
3+5
-
3+1
Add to Reduce
3+5+8
1+4+2
2+5
-
-
8
-
4
Second Total
16
7
7
-
-
-
-
-
Reduce to Deduce
1+6
-
-
-
-
8
-
4
Essence of Number
7
7
7

 

 

O
=
6
-
3
OUT
56
11
2
O
=
6
-
2
OF
21
12
3
S
=
1
-
7
SHADOWS
89
26
8
A
=
1
-
3
AND
19
10
1
P
=
7
-
9
PHANTASMS
111
30
3
I
=
9
-
4
INTO
58
22
4
T
=
2
-
5
TRUTH
87
24
6
-
-
32
-
33
Add to Reduce
441
135
27
-
-
3+2
-
3+3
Reduce to Deduce
4+4+1
1+3+5
2+7
-
-
5
-
6
Essence of Number
9
9
9

 

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
First Total
189
90
18
1+8
Add to Reduce
1+8+9
9+0
1+8
9
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
9
Essence of Number
9
9
9

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN

SWIFT REPEAT SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

Our minds seem to be organised to search for relationships and sequences. We look for hidden orders.

These intuitions seem to be more important than the facts themselves, for there is always the thrill at finding something, a pattern, it is a discovery - what was unknown is now revealed. Imagine looking up at the stars and finding the zodiac!

Searching out patterns is a pure delight.

Suddenly the counters fall into place and a connection is found, not necessarily a geometric one, but a relationship between numbers, pictures of the mind, that were not obvious before. There is that excitement of finding order in something that was otherwise hidden.

And there is the knowledge that a huge unseen world lurks behind the facades we see of the numbers themselves."

 

 

FINGERPRINTS OF THE GODS

A QUEST FOR THE BEGINNING AND THE END

Graham Hancock 1995

Chapter 32

Speaking to the Unborn

Page 285

"It is understandable that a huge range of myths from all over the ancient world should describe geological catastrophes in graphic detail. Mankind survived the horror of the last Ice Age, and the most plausible source for our enduring traditions of flooding and freezing, massive volcanism and devastating earthquakes is in the tumultuous upheavals unleashed during the great meltdown of 15,000 to 8000 BC. The final retreat of the ice sheets, and the consequent 300-400 foot rise in global sea levels, took place only a few thousand years before the beginning of the historical period. It is therefore not surprising that all our early civilizations should have retained vivid memories of the vast cataclysms that had terrified their forefathers.
Much harder to explain is the peculiar but distinctive way the myths of cataclysm seem to bear the intelligent imprint of a guiding hand.l Indeed the degree of convergence between such ancient stories is frequently remarkable enough to raise the suspicion that they must all have been 'written' by the same 'author'.
Could that author have had anything to do with the wondrous deity, or superhuman, spoken of in so many of the myths we have reviewed, who appears immediately after the world has been shattered by a horrifying geological catastrophe and brings comfort and the gifts of civilization to the shocked and demoralized survivors?
White and bearded, Osiris is the Egyptian manifestation of this / Page 286 / universal figure, and it may not be an accident that one of the first acts he is remembered for in myth is the abolition of cannibalism among the primitive inhabitants of the Nile Valley.2 Viracocha, in South America, was said to have begun his civilizing mission immediately after a great flood; Quetzalcoatl, the discoverer of maize, brought the benefits of crops, mathematics, astronomy and a refined culture to Mexico after the Fourth Sun had been overwhelmed by a destroying deluge.
Could these strange myths contain a record of encounters between scattered palaeolithic tribes which survived the last Ice Age and an as yet unidentified high civilization which passed through the same epoch?
And could the myths be attempts to communicate?

A message in the bottle of time"

'Of all the other stupendous inventions,' Galileo once remarked,

what sublimity of mind must have been his who conceived how to communicate his most secret thoughts to any other person, though very distant either in time or place, speaking with those who are in the Indies, speaking to those who are not yet born, nor shall be this thousand or ten thousand years? And with no greater difficulty than the various arrangements of two dozen little signs on paper? Let this be the seal of all the admirable inventions of men.3

If the 'precessional message' identified by scholars like Santillana, von Dechend and Jane Sellers is indeed a deliberate attempt at communication by some lost civilization of antiquity, how come it wasn't just written down and left for us to find? Wouldn't that have been easier than encoding it in myths? Perhaps.
Nevertheless, suppose that whatever the message was written on got destroyed or worn away after many thousands of years? Or suppose that the language in which it was inscribed was later forgotten utterly (like the enigmatic Indus Valley script, which has been studied closely for more than half a century but has so far resisted all attempts at decoding)? It must be obvious that in such circumstances a written / Page 287 / legacy to the future would be of no value at all, because nobody would be able to make sense of it.
What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them - and the city of Teotihuacan may be the calling-card of a lost civilization written in the eternal language of mathematics.
Geodetic data, related to the exact positioning of fixed geographical points and to the shape and size of the earth, would also remain valid and recognizable for tens of thousands of years, and might be most conveniently expressed by means of cartography (or in the construction of giant geodetic monuments like the Great Pyramid of Egypt, as we shall see).
Another 'constant' in our solar system is the language of time: the great but regular intervals of time calibrated by the inch-worm creep of precessional motion. Now, or ten thousand years in the future, a message that prints out numbers like 72 or 2160 or 4320 or 25,920 should be instantly intelligible to any civilization that has evolved a modest talent for mathematics and the ability to detect and measure the almost imperceptible reverse wobble that the sun appears to make along the ecliptic against the background of the fixed stars..."

"What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them"

"WRITTEN IN THE ETERNAL LANGUAGE OF MATHEMATICS"

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

0
-
Z
=
8
-
4
ZERO
64
28
1
1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
42
-
40
Add
522
225
45
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
9
-
-
-
6
-
4
Deduce
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
0
-
Z
=
8
-
4
ZERO
64
28
1
-
1
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
42
-
40
Add
522
225
45
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
4+2
-
4+0
Reduce
5+2+2
2+2+5
4+5
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
6
-
4
Deduce
9
9
9
-
1
4
3
8
5
9
5
8
9

 

 

1
-
O
=
6
-
3
ONE
34
16
7
2
-
T
=
2
-
3
TWO
58
13
4
3
-
T
=
2
-
5
THREE
56
29
2
4
-
F
=
6
-
4
FOUR
60
24
6
5
-
F
=
6
-
4
FIVE
42
24
6
6
-
S
=
1
-
3
SIX
52
16
7
7
-
S
=
1
-
5
SEVEN
65
20
2
8
-
E
=
5
-
5
EIGHT
49
31
4
9
-
N
=
5
-
4
NINE
42
24
6
45
-
-
-
34
-
36
Add
458
197
44
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
9
-
-
-
7
4
9
Deduce
17
17
8
-
-
-
-
-
-
-
Produce
1+7
1+7
-
9
-
-
-
7
-
9
Essence
8
8
8

 

 

-
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
O
=
6
-
3
ONE
34
16
7
-
-
-
-
-
-
-
7
-
-
2
-
T
=
2
-
3
TWO
58
13
4
-
-
-
-
4
-
-
-
-
-
3
-
T
=
2
-
5
THREE
56
29
2
-
-
2
-
-
-
-
-
-
-
4
-
F
=
6
-
4
FOUR
60
24
6
-
-
-
-
-
-
6
-
-
-
5
-
F
=
6
-
4
FIVE
42
24
6
-
-
-
-
-
-
6
-
-
-
6
-
S
=
1
-
3
SIX
52
16
7
-
-
-
-
-
-
-
7
-
-
7
-
S
=
1
-
5
SEVEN
65
20
2
-
-
2
-
-
-
-
-
-
-
8
-
E
=
5
-
5
EIGHT
49
31
4
-
-
-
-
4
-
-
-
-
-
9
-
N
=
5
-
4
NINE
42
24
6
-
-
-
-
-
-
6
-
-
-
45
-
-
-
34
-
36
Add
458
197
44
-
1
4
3
8
5
18
14
8
9
4+5
-
-
-
3+4
-
3+6
Reduce
4+5+8
1+9+7
4+4
-
-
-
-
-
-
1+8
1+4
-
-
9
-
-
-
7
4
9
Deduce
17
17
8
-
1
4
3
8
5
18
14
8
9
-
-
-
-
-
-
-
Produce
1+7
1+7
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
7
-
9
Essence
8
8
8
-
1
4
3
8
5
9
5
8
9

 

 

0
-
4
ZERO
8
5
9
6
-
=
28
2+8
=
10
1+0
1
1
-
3
ONE
6
5
5
-
-
=
16
1+6
=
7
-
7
2
-
3
TWO
2
5
6
-
-
=
13
1+3
=
4
-
4
3
-
5
THREE
2
8
9
5
5
=
29
2+9
=
11
1+1
2
4
-
4
FOUR
6
6
3
9
-
=
24
2+4
=
6
-
6
5
-
4
FIVE
6
9
4
5
-
=
24
2+4
=
6
-
6
6
-
3
SIX
1
9
6
-
-
=
16
1+6
=
7
-
7
7
-
5
SEVEN
1
5
4
5
5
=
20
2+0
=
2
-
2
8
-
5
EIGHT
5
9
7
8
2
=
31
3+1
=
4
-
4
9
-
4
NINE
5
9
5
5
-
=
24
2+4
=
6
-
6
45
-
40
Add
42
70
58
43
12
-
225
-
-
63
-
45
4+5
-
4+0
-
4+2
7+0
5+8
4+3
1+2
-
2+2+5
-
-
6+3
-
4+5
9
-
4
Reduce
6
7
13
7
3
-
9
-
-
9
-
9
-
-
-
-
-
-
1+3
-
-
-
-
-
-
-
-
-
9
-
4
Deduce
6
7
4
7
3
-
9
-
-
9
-
9

 

 

 

The Upside Down of the Downside Up

 

 

THE DEATH OF GODS IN ANCIENT EGYPT

Jane B. Sellars 1992

Page 204

"The overwhelming awe that accompanies the realization, of the measurable orderliness of the universe strikes modern man as well. Admiral Weiland E. Byrd, alone In the Antarctic for five months of polar darkness, wrote these phrases of intense feeling:

Here were the imponderable processes and forces of the cosmos, harmonious and soundless. Harmony, that was it! I could feel no doubt of oneness with the universe. The conviction came that the rhythm was too orderly. too harmonious, too perfect to be a product of blind chance - that, therefore there must be purpose in the whole and that man was part of that whole and not an accidental offshoot. It was a feeling that transcended reason; that went to the heart of man's despair and found it groundless. The universe was a cosmos, not a chaos; man was as rightfully a part of that cosmos as were the day and night.10

Returning to the account of the story of Osiris, son of Cronos god of' Measurable Time, Plutarch takes, pains to remind the reader of the original Egyptian year consisting of 360 days.

Phrases are used that prompt simple mental. calculations and an attention to numbers, for example, the 360-day year is described as being '12 months of 30 days each'. Then we are told that, Osiris leaves on a long journey, during which Seth, his evil brother, plots with 72 companions to slay Osiris: He also secretly obtained the measure of Osiris and made ready a chest in which to entrap him.

The, interesting thing about this part of the-account is that nowhere in the original texts of the Egyptians are we told that Seth, has 72 companions. We have already been encouraged to equate Osiris with the concept of measured time; his father being Cronos. It is also an observable fact that Cronos-Saturn has the longest sidereal period of the known planets at that time, an orbit. of 30 years. Saturn is absent from a specific constellation for that length of time.

A simple mathematical fact has been revealed to any that are even remotely sensitive to numbers: if you multiply 72 by 30, the years of Saturn's absence (and the mention of Osiris's absence prompts one to recall this other), the resulting product is 2,160: the number of years required, for one 30° shift, or a shift: through one complete sign of the zodiac. This number multplied by the /Page205 / 12 signs also gives 25,920. (And Plutarch has reminded us of 12)

If you multiply the unusual number 72 by 360, a number that Plutarch mentions several times, the product will be 25,920, again the number of years symbolizing the ultimate rebirth.

This 'Eternal Return' is the return of, say, Taurus to the position of marking the vernal equinox by 'riding in the solar bark with. Re' after having relinquished this honoured position to Aries, and subsequently to the to other zodiacal constellations.

Such a return after 25,920 years is indeed a revisit to a Golden Age, golden not only because of a remarkable symmetry In the heavens, but golden because it existed before the Egyptians experienced heaven's changeability.

But now to inform the reader of a fact he or she may already know. Hipparaus did: not really have the exact figures: he was a trifle off in his observations and calculations. In his published work, On the Displacement of the Solstitial and Equinoctial Signs, he gave figures of 45" to 46" a year, while the truer precessional lag along the ecliptic is about 50 seconds. The exact measurement for the lag, based on the correct annual lag of 50'274" is 1° in 71.6 years, or 36in 25,776 years, only 144 years less than the figure of 25,920.

With Hipparchus's incorrect figures a 'Great Year' takes from 28,173.9 to 28,800 years, Incorrect by a difference of from 2,397.9 years to 3,024.

Since Nicholas Copernicus (AD 1473-1543) has always been credited with giving the correct numbers (although Arabic astronomer Nasir al-Din Tusi,11 born AD 1201, is known to have fixed the Precession at 50°), we may correctly ask, and with justifiable astonishment 'Just whose information was Plutarch transmitting'

AN IMPORTANT POSTSCRIPT

Of course, using our own notational system, all the important numbers have digits that reduce to that amazing number 9 a number that has always delighted budding mathematician.

Page 206

Somewhere along the way, according to Robert Graves, 9 became the number of lunar wisdom.12

This number is found often in the mythologies of the world. the Viking god Odin hung for nine days and nights on the World Tree in order to acquire the secret of the runes, those magic symbols out of which writing and numbers grew. Only a terrible sacrifice would give away this secret, which conveyed upon its owner power and dominion over all, so Odin hung from his neck those long 9 days and nights over the 'bottomless abyss'. In the tree were 9 worlds, and another god was said to have been born of 9 mothers.

Robert Graves, in his White Goddess, Is intrigued by the seemingly recurring quality of the number 72 in early myth and ritual. Graves tells his reader that 72 is always connected with the number 5, which reflects, among other things, the five Celtic dialects that he was investigating. Of course, 5 x 72= 360, 360 x 72= 25,920. Five is also the number of the planets known to the ancient world, that is, Saturn, Jupiter, Mars, Venus Mercury.

Graves suggests a religious mystery bound up with two ancient Celtic 'Tree Alphabets' or cipher alphabets, which as genuine articles of Druidism were orally preserved and transmitted for centuries. He argues convincingly that the ancient poetry of Europe was ultimately based on what its composers believed to be magical principles, the rudiments of which formed a close religious secret for centuries. In time these were-garbled, discredited and forgotten.

Among the many signs of the transmission of special numbers he points out that the aggregate number of letter strokes for the complete 22-letter Ogham alphabet that he is studying is 72 and that this number is the multiple of 9, 'the number of lunar wisdom'. . . . he then mentions something about 'the seventy day season during which Venus moves successively from. maximum eastern elongation 'to inferior conjunction and maximum western elongation'.13

Page 207

"...Feniusa Farsa, Graves equates this hero with Dionysus Farsa has 72 assistants who helped him master the 72 languages created at the confusion of Babel, the tower of which is said to be built of 9 different materials

We are also reminded of the miraculous translation into Greek of the Five Books of Moses that was done by 72 scholars working for 72 days, Although the symbol for the Septuagint is LXX, legend, according to the fictional letter of Aristeas, records 72. The translation was done for Ptolemy Philadelphus (c.250 BC), by Hellenistic Jews, possibly from Alexandra.14

Graves did not know why this number was necessary, but he points out that he understands Frazer's Golden Bough to be a a book hinting that 'the secret involves the truth that the Christian dogma, and rituals, are the refinement of a great body of primitive beliefs, and that the only original element in Christianity- is the personality of Christ.15

Frances A. Yates, historian of Renaissance hermetisma tells, us the cabala had 72 angels through which the sephiroth (the powers of God) are believed to be approached, and further, she supplies the information that although the Cabala supplied a set of 48 conclusions purporting to confirm the Christian religion from the foundation of ancient wisdom, Pico Della Mirandola, a Renaissance magus, introduced instead 72, which were his 'own opinion' of the correct number. Yates writes, 'It is no accident there are seventy-two of Pico's Cabalist conclusions, for the conclusion shows that he knew something of the mystery of the Name of God with seventy-two letters.'16

In Hamlet's Mill de Santillarta adds the facts that 432,000 is the number of syllables in the Rig-Veda, which when multiplied by the soss (60) gives 25,920" (The reader is forgiven for a bit of laughter at this point)

Thee Bible has not escaped his pursuit. A prominent Assyriologist of the last century insisted that the total of the years recounted
mounted in Genesis for the lifetimes of patriarchs from the Flood also contained the needed secret numbers. (He showed that in the 1,656.years recounted in the Bible there are 86,400 7 day weeks, and dividing this number yields / Page 208 / 43,200.) In Indian yogic schools it is held that all living beings exhale and inhale 21,600 times a day, .multiply this by 2 and again we have.the necessary 432 digits.

Joseph Campbell discerns the secret in the date set for the coming of Patrick to Ireland. Myth-gives this date-as.- the interest-
ing number of AD.432.18

Whatever one may think-of some of these number coincidences, it becomes. difficult to escape the suspicion that many signs (number and otherwise) -indicate that early man observed the results.. of the movement of Precession . and that the-.transmission of this information was .considered of prime importance.

'With the awareness of the phenomenon, observers would certainly have tried for its measure, and such an endeavour would
have constituted the construction-of a 'Unified Field Theory' for nothing .less than Creation itself. Once determined, it would have been information worthy of secrecy and worthy of the passing on to future adepts.

But one last word about mankind's romance with number coincidences.The antagonist in John Updike's novel, Roger's Version, is a computer hacker, who, convinced.,that scientific evidence of God's existence is accumulating, endeavours to prove it by feeding -all the available scientific information. into a comuter. In his search for God 'breaking, through', he has become fascinated by certain numbers that have continually been cropping up. He explains them excitedly as 'the terms of Creation':

"...after a while I noticed that all over the sheet there seemed to hit these twenty-fours Jumping out at me. Two four; two,four.Planck time, for instance, divided by the radiation constant yields a figure near eight times ten again to the negative twenty-fourth, and the permittivity of free space, or electric constant, into the Bohr radiusekla almost exactly six times ten to the negative twenty-fourth. On positive side, the electromagnetic line-structure constant times Hubble radius - that is, the size of the universe as we now perceive it gives us something quite close to ten to the twenty-fourth, and the strong-force constant times the charge on the proton produces two point four times ten to the negative eighteenth, for another I began to circle twenty-four wherever it appeared on the Printout here' - he held it up. his piece of striped and striped wallpaper, decorated / Page 209 / with a number of scarlet circles - 'you can see it's more than random.'19
This inhabitant of the twentieth century is convinced that the striking occurrences of 2 and 4 reveal the sacred numbers by which God is speaking to us.

So much for any scorn directed to ancient man's fascination with number coincidences. That fascination is alive and well, Just a bit more incomprehensible"

 

 

All about the planets in our Solar System. The nine planets that orbit the sun are (in order from the sun): Mercury,Venus, Earth, Mars, Jupiter, Saturn, ... www.enchantedlearning.com/subjects/astronomy/planets

Our solar system consists of the sun, eight planets, moons, dwarf planets, an asteroid belt, comets, meteors, and others. The sun is the center of our solar system; the planets, their moons, the asteroids, comets, and other rocks and gas all orbit the sun.

The nine planets that orbit the sun are (in order from the sun): Mercury,Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto (a dwarf planet). A belt of asteroids (minor planets made of rock and metal) lies between Mars and Jupiter. These objects all orbit the sun in roughly circular orbits that lie in the same plane, the ecliptic (Pluto is an exception; it has an elliptical orbit tilted over 17° from the ecliptic).

 

 

LOOK AT THE NINES LOOK AT THE NINES LOOK AT THE NINES

THE NINES THE NINES THE NINES

 

 

OSIRIS LORD OF THE LABYRINTH

WHO ART THOU LORD

 

 

I

I SAY I

LOVE ORDER GODS ORDER I LOVE

 

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

 

15
THE RAINBOW LIGHT
-
-
-
-
THE
33
15
6
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
-
L
12
3
3
-
I
9
9
9
-
G+H+T
35
17
8
15
THE RAINBOW LIGHT
171
81
54
1+5
-
1+7+1
8+1
5+4
6
THE RAINBOW LIGHT
9
9
9

 

 

THE LIGHT IS RISING NOW RISING IS THE LIGHT

 

 

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
=
7
=
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
=
7
=
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
=
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
=
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
=
9
=
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
=
9
=
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
=
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

CONVOLVULUS
BEELZEBUB
I, AM, THE, GOD, THAT, IS
INVINCIBLE, I, NV, I, NC, I, BLE
I, THANK, THE, ANKH, THE, ANKH, I, THANK
GENTLE
EVOLVE LOVE LOVE EVOLVE
LOVE EVOLVE
ALLAHU, AKBAR
GOD, IS, GREAT
ALLAH, ALL, AH
ALL, ARE, HE
HALAL, ALLAH
EACH, FOR, ALL, ALL, FOR, GOD
YOU, I, ME, THE, HERE, WE, GO, EGO
THE, OVER, LOADED, EGO
CHANGING
COMFORT
HEART, ART
WITH, FIRST, CONTACT, ALIEN, ALIENS
FAIRY, I, R, FAY
ANAELLE
A, FAIRY, CHILD, AND, FULL, OF, WOE
A, FAERIES, CHILD, AND, FULL, OF GLOW
A, FAIRY, CHILD, AND, FULL, OF, GLOW
LIVE, EVIL, VEIL, BURKA, NIQAB
THE, HASTENING, WHILE
THE HASTENING WHILE
FOLLOW, FOLLOWS, FOLLOWING, FOLLOWED
ELECTRIC = ET CIRCLE = ELECTRIC
CIRCLE ELECTRIC = ET CIRCLE = ELECTRIC
THE, LAMB OF, GOD
THE LAMB OF GOD
PRIDE, GLUTTONY, GREED, WRATH, ENVY, LUST, SLOTH
EPIPHANY
FREE, GRATIS
THOU, HAST, BEEN, WEIGHED, IN, THE, BALANCE, AND,
FOUND, WANTING
THOU, HAST
DULCE, ET, DECORUM, EST
DEATH, RIDES, A, PALE,HORSE
GARIBALDI, GIUSEPPE
LOOK ABROAD THROUGH NATURE'S RANGE

 

 

LOOK ABROAD THROUGH NATURE'S RANGE NATURE'S MIGHTY LAW IS CHANGE

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
L
=
3
-
4
LOOK
53
17
8
-
-
-
-
-
-
-
-
8
-
A
=
1
-
6
ABROAD
41
23
5
-
-
-
-
-
5
-
-
-
-
T
=
2
-
7
THROUGH
97
43
7
-
-
-
-
-
-
-
7
-
-
N
=
5
-
7
NATURES
98
26
8
-
-
-
-
-
-
-
-
8
-
R
=
9
-
5
RANGE
45
27
9
-
-
-
-
-
-
-
-
-
9
N
=
5
-
7
NATURES
98
26
8
-
-
-
-
-
-
-
-
8
-
M
=
4
-
6
MIGHTY
82
37
1
-
1
-
-
-
-
-
-
-
-
L
=
3
-
3
LAW
36
9
9
-
-
-
-
-
-
-
-
-
9
I
=
9
-
2
IS
28
10
1
-
1
-
-
-
-
-
-
-
-
C
=
3
-
6
CHANGE
38
29
2
-
-
2
-
-
-
-
-
-
-
-
-
44
-
53
Add
616
247
58
-
2
2
3
4
5
6
7
24
18
-
-
4+4
-
5+3
Reduce
6+1+6
2+4+7
5+8
-
-
-
-
-
-
-
-
2+4
1+8
-
-
8
4
8
Deduce
13
13
4
-
2
2
3
4
5
6
7
6
9
-
-
-
-
-
Produce
1+3
1+3
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
8
Essence
4
4
4
-
2
2
3
4
5
6
7
6
9

 

 

-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
B
=
2
-
2
BY
27
9
9
T
=
2
-
5
THEIR
60
33
6
D
=
4
-
5
DEEDS
37
19
1
Y
=
7
-
2
YE
30
12
3
S
=
1
-
5
SHALL
52
16
7
K
=
2
-
4
KNOW
63
18
9
T
=
2
-
4
THEM
46
19
1
-
-
20
-
27
Reduce
315
126
36
-
-
2+0
-
2+7
Deduce
3+1+5
1+2+6
3+6
-
-
2
-
9
Essence
9
9
9

 

 

Convolvulus - Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Convolvulus

Convolvulus /kənˈvɒlvjuːləs/ is a genus of about 200 to 250 species of flowering plants in the bindweed family Convolvulaceae, with a cosmopolitan ...
Convolvulus arvensis - ‎Convolvulus tricolor - ‎Convolvulus cneorum

 

 

Agrius convolvuli - Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Agrius_convolvuli

Distribution map. The Convolvulus Hawk-moth, Agrius convolvuli, is a large hawk-moth. It is common throughout Europe, Africa and Australia. partly as a migrant ...

 

-
-
-
-
-
CONVOLVULUS
-
-
-
C
=
3
-
1
C
3
3
3
O
=
6
-
1
O
15
6
6
N
=
5
-
1
N
14
5
5
V
=
4
-
1
V
22
4
4
O
=
6
-
1
O
15
6
6
L
=
3
-
1
L
12
3
3
V
=
4
-
1
V
22
4
4
U
=
3
-
1
U
21
3
3
L
=
3
-
1
L
12
3
3
U
=
3
-
1
U
21
3
3
S
=
1
-
1
S
19
10
1
-
-
41
4
11
CONVOLVULUS
176
41
41
-
-
4+1
-
1+1
-
1+7+6
4+1
4+1
Q
-
5
-
2
CONVOLVULUS
14
5
5
-
-
-
-
4
-
1+4
-
-
-
-
5
5
2
CONVOLVULUS
5
5
5

 

 

C
=
3
-
-
CONVOLVULUS
-
-
-
-
-
-
-
2
C+O
18
9
9
-
-
-
-
2
N+V
36
9
9
-
-
-
-
2
O+L
27
9
9
-
-
-
-
1
V
22
4
4
-
-
-
-
3
U+L+U
54
9
9
-
-
-
-
1
S
19
10
1
C
=
3
4
11
CONVOLVULUS
176
41
41
-
-
-
-
1+1
-
1+7+6
4+1
4+1
C
=
3
-
2
CONVOLVULUS
14
5
5
-
-
-
-
4
-
1+4
-
-
C
=
3
5
2
CONVOLVULUS
5
5
5

 

 

-
BEELZEBUB
-
-
-
1
B
2
2
2
1
E
5
5
5
1
E
5
5
5
2
L+Z
38
11
2
1
E
5
5
5
1
B
2
2
2
1
U
21
3
3
1
B
2
2
2
9
BEELZEBUB
80
35
26
-
-
8+0
3+5
2+6
9
BEELZEBUB
8
8
8

 

 

-
9
B
E
E
L
Z
E
B
U
B
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
8
-
=
8
=
8
=
8
-
`-
-
-
-
-
26
-
-
-
-
+
=
26
2+6
=
8
=
8
=
8
-
9
B
E
E
L
Z
E
B
U
B
-
-
-
-
-
--
-
-
-
-
-
-
2
5
5
3
-
5
2
3
2
+
=
27
2+7
=
9
=
9
=
9
-
`-
2
5
5
12
-
5
2
21
2
+
=
54
5+4
=
9
=
9
=
9
-
9
B
E
E
L
Z
E
B
U
B
-
-
-
-
-
--
-
-
-
-
-
`-
2
5
5
12
26
5
2
21
2
+
=
80
8+0
=
8
=
8
=
8
-
-
2
5
5
3
8
5
2
3
2
+
=
35
3+5
=
8
=
8
=
8
-
9
B
E
E
L
Z
E
B
U
B
T
-
-
-
-
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-2-
-
2
-
-
-
-
-
2
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
3
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
--
-
5
5
-
-
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
--
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
17
9
B
E
E
L
Z
E
B
U
B
-
-
28
-
-
9
-
35
-
26
1+7
-
-
-
-
-
-
-
-
-
-
-
-
2+8
-
-
-
-
3+5
-
2+6
8
9
B
E
E
L
Z
E
B
U
B
-
-
10
-
-
9
-
8
-
8
-
-
2
5
5
3
8
5
2
3
2
-
-
1+0
-
-
-
-
-
-
-
8
9
B
E
E
L
Z
E
B
U
B
-
-
1
-
-
9
-
8
-
8

 

 

9
B
E
E
L
Z
E
B
U
B
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
-
-
+
=
8
-
=
8
=
8
=
8
`-
-
-
-
-
26
-
-
-
-
+
=
26
2+6
=
8
=
8
=
8
9
B
E
E
L
Z
E
B
U
B
-
-
-
-
-
--
-
-
-
-
-
2
5
5
3
-
5
2
3
2
+
=
27
2+7
=
9
=
9
=
9
`-
2
5
5
12
-
5
2
21
2
+
=
54
5+4
=
9
=
9
=
9
9
B
E
E
L
Z
E
B
U
B
-
-
-
-
-
--
-
-
-
-
`-
2
5
5
12
26
5
2
21
2
+
=
80
8+0
=
8
=
8
=
8
-
2
5
5
3
8
5
2
3
2
+
=
35
3+5
=
8
=
8
=
8
9
B
E
E
L
Z
E
B
U
B
T
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
3
-
-
-
3
-
-
-
3
occurs
x
2
=
6
=
6
--
-
5
5
-
-
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
--
-
-
-
-
8
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
B
E
E
L
Z
E
B
U
B
-
-
28
-
-
9
-
35
-
26
-
-
-
-
-
-
-
-
-
-
-
-
2+8
-
-
-
-
3+5
-
2+6
9
B
E
E
L
Z
E
B
U
B
-
-
10
-
-
9
-
8
-
8
-
2
5
5
3
8
5
2
3
2
-
-
1+0
-
-
-
-
-
-
-
9
B
E
E
L
Z
E
B
U
B
-
-
1
-
-
9
-
8
-
8

 

 

1
I
9
9
9
2
AM
14
5
5
3
THE
33
15
6
3
GOD
26
17
8
4
THAT
49
13
4
2
IS
28
10
1

 

 

-
INVINCIBLE
-
-
-
1
I
9
9
9
2
N+V
36
9
9
1
I
9
9
9
2
N+C
17
8
8
1
I
9
9
9
3
B+L+E
19
10
1
10
INVINCIBLE
99
54
45
1+0
-
9+9
5+4
4+5
1
INVINCIBLE
18
9
9
-
-
1+8
-
-
1
INVINCIBLE
9
9
9

 

 

1
I
9
9
9
5
THANK
54
18
9
3
THE
33
15
6
4
ANKH
34
16
7
3
THE
33
15
6
4
ANKH
34
16
7
1
I
9
9
9
5
THANK
54
18
9

 

 

6
GENTLE
63
27
9

 

 

LOVELESS HEARTS SHALL LOVE
TOMORROW, HEARTS THAT HAVE
LOVED SHALL LOVE ANEW,
SP
RING IS YOUNG NOW, SPRING
IS SINGING, IN THE SPRING
THE
WORLD FIRST GREW.

Anonymous – Latin about 4th century

 

4
LIVE
48
21
3
1
I
9
9
9
1
O
15
6
6
4
LOVE
54
18
9
10
Add to Reduce
126
54
27
1+0
Reduce to Deduce
1+2+6
5+4
2+7
1
Essence of Number
9
9
9

 

 

-
LOVE
--
-
-
2
L+O
27
9
9
2
V+E
27
9
9
4
LOVE
54
18
18
-
-
5+4
1+8
1+8
4
LOVE
9
9
9

 


“Ah! Sweet Mystery of Life” | National Museum of American ...

“Ah! Sweet Mystery of Life.” Rida Johnson Young wrote the lyrics of the song and Victor Herbert composed the music. The song came from Hebert’s operetta Naughty Marietta, one of his greatest successes. Sheet music published in 1910


AH! SWEET MYSTERY OF LIFE AT LAST I'VE FOUND THEE

AH! I KNOW AT LAST THE SECRET OF IT ALL;

ALL THE LONGING, SEEKING, STRIVING, WAITING, YEARNING

THE BURNING HOPES, THE JOY AND IDLE TEARS THAT FALL!

FOR 'TIS LOVE, AND LOVE ALONE, THE WORLD IS SEEKING,

AND 'TIS LOVE, AND LOVE ALONE, THAT CAN REPAY!

'TIS THE ANSWER, 'TIS THE END AND ALL OF LIVING

FOR IT IS LOVE ALONE THAT RULES FOR AYE!

LOVE AND LOVE ALONE, THE WORLD IS SEEKING,

FOR 'TIS LOVE, AND LOVE ALONE, THAT CAN REPAY!

'TIS THE ANSWER, 'TIS THE END AND ALL OF LIVING

FOR IT IS LOVE ALONE THAT RULES FOR AYE

 


AHSWEET MYSTERY OF LIFE AT LAST I'VE FOUND THEE

AH! I KNOW AT LAST THE SECRET OF IT ALL;

 

A
=
1
-
2
AH
9
9
9
S
=
1
-
5
SWEET
72
18
9
M
=
4
-
7
MYSTERY
125
35
8
O
=
6
-
2
OF
21
12
3
L
=
3
-
4
LIFE
32
23
5
A
=
1
-
2
AT
21
3
3
L
=
3
-
4
LAST
52
7
7
I
=
9
-
3
I'VE
36
18
9
F
=
6
-
5
FOUND
60
24
6
T
=
2
-
4
THEE
38
20
2
-
-
36
-
38
-
466
169
61
A
=
1
-
2
AH
9
9
9
I
=
9
-
1
I
9
9
9
K
=
2
-
4
KNOW
63
18
9
A
=
1
-
2
AT
21
3
3
L
=
3
-
4
LAST
52
7
7
T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SECRET
70
25
7
O
=
6
-
2
OF
21
12
3
I
=
9
-
2
IT
29
11
2
A
=
1
-
3
ALL
25
7
7
-
-
36
-
29
-
332
116
62
-
-
-
-
-
-
-
-
-
-
-
71
1
67
1
798
285
123
-
-
7+1
-
6+7
-
7+9+8
2+8+5
1+2+3
-
-
8
1
13
1
24
15
6
-
-
-
-
1+3
-
2+4
1+5
-
-
-
8
1
4
1
6
6
6

 

 

-
LOVE EVOLVE LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
2
L+O
27
9
9
2
V+E
27
9
9
14
LOVE EVOLVE LOVE
189
63
63
1+4
-
1+8+9
6+3
6+3
5
LOVE EVOLVE LOVE
18
9
9
-
-
1+8
-
-
5
LOVE EVOLVE LOVE
9
9
9

 

 

-
EVOLVE LOVE EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
2
L+O
27
9
9
2
V+E
27
9
9
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
16
EVOLVE LOVE EVOLVE
216
72
72
1+6
-
2+1+6
7+2
7+2
7
EVOLVE LOVE EVOLVE
9
9
9
-
-
-
-
-
7
EVOLVE LOVE EVOLVE
9
9
9

 

 

-
LOVE EVOLVE LOVE
-
-
-
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
-
EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
-
EVOLVE
-
-
-
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
14
LOVE EVOLVE LOVE
189
63
63
1+4
-
1+8+9
6+3
6+3
5
LOVE EVOLVE LOVE
18
9
9
-
-
1+8
-
-
5
LOVE EVOLVE LOVE
9
9
9

 

 

-
4
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
6
-
-
+
=
6
-
=
6
=
6
-
-
-
15
-
-
+
=
15
1+5
=
6
=
6
-
4
L
O
V
E
-
-
-
-
-
-
-
-
-
-
3
-
4
5
+
=
12
1+2
=
3
=
3
-
-
12
-
22
5
+
=
39
3+9
=
12
1+2
3
-
4
L
O
V
E
-
-
-
-
-
-
-
-
-
-
12
15
22
5
+
=
54
5+4
=
9
=
9
-
-
3
6
4
5
+
=
18
1+8
=
9
=
9
-
4
L
O
V
E
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
ONE
1
-
-
-
2
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
-
6
-
-
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
9
NINE
9
-
-
-
27
4
L
O
V
E
-
-
18
-
-
4
-
18
2+7
-
-
-
-
-
-
-
1+8
-
-
-
-
1+8
9
4
L
O
V
E
-
-
9
-
-
4
-
9
-
-
3
6
4
5
-
-
-
-
-
-
-
-
9
4
L
O
V
E
-
-
9
-
-
4
-
9

 

 

4
L
O
V
E
-
-
-
-
-
-
-
-
-
-
6
-
-
+
=
6
-
=
6
=
6
-
-
15
-
-
+
=
15
1+5
=
6
=
6
4
L
O
V
E
-
-
-
-
-
-
-
-
-
3
-
4
5
+
=
12
1+2
=
3
=
3
-
12
-
22
5
+
=
39
3+9
=
12
1+2
3
4
L
O
V
E
-
-
-
-
-
-
-
-
-
12
15
22
5
+
=
54
5+4
=
9
=
9
-
3
6
4
5
+
=
18
1+8
=
9
=
9
4
L
O
V
E
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
-
-
-
4
-
-
-
4
occurs
x
1
=
4
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
6
-
-
-
-
6
occurs
x
1
=
6
4
L
O
V
E
-
-
18
-
-
4
-
18
-
-
-
-
-
-
-
1+8
-
-
-
-
1+8
4
L
O
V
E
-
-
9
-
-
4
-
9
-
3
6
4
5
-
-
-
-
-
-
-
-
4
L
O
V
E
-
-
9
-
-
4
-
9

 

 

-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
4
LOVE
54
18
18
-
-
5+4
1+8
1+8
4
LOVE
9
9
9
-
-
-
-
-
-
-
-
-
-
-
EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
6
EVOLVE
81
27
27
-
-
8+1
2+7
2+7
6
EVOLVE
9
9
9

 

 

-
10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
+
=
12
1+2
=
3
=
3
=
3
-
-
-
15
-
-
-
-
-
15
-
-
-
+
=
30
3+0
=
3
=
3
=
3
-
10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
4
5
-
5
4
-
3
4
5
+
=
33
3+3
=
6
=
6
=
6
-
-
12
-
22
5
-
5
22
-
12
22
5
+
=
105
1+0+5
=
6
=
6
=
6
-
10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
12
15
22
5
-
5
22
15
12
22
5
+
=
135
1+3+5
=
9
=
9
=
9
-
-
3
6
4
5
-
5
4
6
3
4
5
+
=
45
4+5
=
9
=
9
=
9
-
10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
Q
-
-
-
4
-
-
-
4
-
-
4
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
5
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
27
10
L
O
V
E
-
E
V
O
L
V
E
-
-
18
-
-
10
-
45
-
18
2+7
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1+8
-
-
1+0
-
4+5
-
1+8
9
1
L
O
V
E
-
E
V
O
L
V
E
-
-
9
-
-
1
-
9
-
9
-
-
3
6
4
5
-
5
4
6
3
4
5
-
-
-
-
-
-
-
-
-
-
9
1
L
O
V
E
-
E
V
O
L
V
E
-
-
9
-
-
1
-
9
-
9

 

 

10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
+
=
12
1+2
=
3
=
3
=
3
-
-
15
-
-
-
-
-
15
-
-
-
+
=
30
3+0
=
3
=
3
=
3
10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
3
-
4
5
-
5
4
-
3
4
5
+
=
33
3+3
=
6
=
6
=
6
-
12
-
22
5
-
5
22
-
12
22
5
+
=
105
1+0+5
=
6
=
6
=
6
10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
12
15
22
5
-
5
22
15
12
22
5
+
=
135
1+3+5
=
9
=
9
=
9
-
3
6
4
5
-
5
4
6
3
4
5
+
=
45
4+5
=
9
=
9
=
9
10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
4
-
-
-
4
-
-
4
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
5
-
5
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
10
L
O
V
E
-
E
V
O
L
V
E
-
-
18
-
-
10
-
45
-
18
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1+8
-
-
1+0
-
4+5
-
1+8
1
L
O
V
E
-
E
V
O
L
V
E
-
-
9
-
-
1
-
9
-
9
-
3
6
4
5
-
5
4
6
3
4
5
-
-
-
-
-
-
-
-
-
-
1
L
O
V
E
-
E
V
O
L
V
E
-
-
9
-
-
1
-
9
-
9

 

 

10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
+
=
12
1+2
=
3
=
3
=
3
-
-
15
-
-
-
-
-
15
-
-
-
+
=
30
3+0
=
3
=
3
=
3
10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
3
-
4
5
-
5
4
-
3
4
5
+
=
33
3+3
=
6
=
6
=
6
-
12
-
22
5
-
5
22
-
12
22
5
+
=
105
1+0+5
=
6
=
6
=
6
10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
--
-
-
-
-
-
12
15
22
5
-
5
22
15
12
22
5
+
=
135
1+3+5
=
9
=
9
=
9
-
3
6
4
5
-
5
4
6
3
4
5
+
=
45
4+5
=
9
=
9
=
9
10
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
4
-
-
-
4
-
-
4
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
5
-
5
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
10
L
O
V
E
-
E
V
O
L
V
E
-
-
18
-
-
10
-
45
-
18
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1+8
-
-
1+0
-
4+5
-
1+8
1
L
O
V
E
-
E
V
O
L
V
E
-
-
9
-
-
1
-
9
-
9
-
3
6
4
5
-
5
4
6
3
4
5
-
-
-
-
-
-
-
-
-
-
1
L
O
V
E
-
E
V
O
L
V
E
-
-
9
-
-
1
-
9
-
9

 

 

-
LOVE EVOLVE LOVE
-
-
-
4
LOVE
54
18
9
6
EVOLVE
81
27
9
4
LOVE
54
18
9
14
LOVE EVOLVE LOVE
189
63
27
1+4
-
1+8+9
6+3
2+7
5
LOVE EVOLVE LOVE
18
9
9
-
-
1+8
-
-
5
LOVE EVOLVE LOVE
9
9
9

 

 

-
LOVE EVOLVE LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
2
L+O
27
9
9
2
V+E
27
9
9
14
LOVE EVOLVE LOVE
189
63
63
1+4
-
1+8+9
6+3
6+3
5
LOVE EVOLVE LOVE
18
9
9
-
-
1+8
-
-
5
LOVE EVOLVE LOVE
9
9
9

 

 

-
EVOLVE LOVE EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
2
L+O
27
9
9
2
V+E
27
9
9
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
16
EVOLVE LOVE EVOLVE
216
72
72
1+6
-
2+1+6
7+2
7+2
7
EVOLVE LOVE EVOLVE
9
9
9
-
-
-
-
-
7
EVOLVE LOVE EVOLVE
9
9
9

 

 

-
LOVE EVOLVE LOVE
-
-
-
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
-
EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
-
EVOLVE
-
-
-
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
14
LOVE EVOLVE LOVE
189
63
63
1+4
-
1+8+9
6+3
6+3
5
LOVE EVOLVE LOVE
18
9
9
-
-
1+8
-
-
5
LOVE EVOLVE LOVE
9
9
9

 

 

-
14
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
-
-
+
=
18
1+8
=
9
=
9
=
9
-
-
-
15
-
-
-
-
-
15
-
-
-
-
-
15
-
-
+
=
45
4+5
=
9
=
9
=
9
-
14
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
4
5
-
5
4
-
3
4
5
-
3
-
4
5
+
=
45
4+5
=
9
=
9
=
9
-
-
12
-
22
5
-
5
22
-
12
22
5
-
12
-
22
5
+
=
144
1+4+4
=
9
=
9
=
9
-
14
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
-
12
15
22
5
-
5
22
15
12
22
5
-
12
15
22
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
-
3
6
4
5
-
5
4
6
3
4
5
-
3
6
4
5
+
=
63
6+3
=
9
=
9
=
9
-
14
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
4
-
-
-
4
-
-
4
-
-
-
-
4
-
-
-
4
occurs
x
4
=
16
1+6
7
-
-
-
-
-
5
-
5
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
27
14
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
18
-
-
14
-
63
-
27
2+7
1+4
3
6
4
5
-
5
4
6
3
4
5
-
3
6
4
5
-
-
1+8
-
-
1+4
-
6+3
-
2+7
9
5
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
9
-
-
5
-
9
-
9

 

 

14
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
-
-
+
=
18
1+8
=
9
=
9
=
9
-
-
15
-
-
-
-
-
15
-
-
-
-
-
15
-
-
+
=
45
4+5
=
9
=
9
=
9
14
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
3
-
4
5
-
5
4
-
3
4
5
-
3
-
4
5
+
=
45
4+5
=
9
=
9
=
9
-
12
-
22
5
-
5
22
-
12
22
5
-
12
-
22
5
+
=
144
1+4+4
=
9
=
9
=
9
14
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
12
15
22
5
-
5
22
15
12
22
5
-
12
15
22
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
3
6
4
5
-
5
4
6
3
4
5
-
3
6
4
5
+
=
63
6+3
=
9
=
9
=
9
14
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
4
-
-
-
4
-
-
4
-
-
-
-
4
-
-
-
4
occurs
x
4
=
16
1+6
7
-
-
-
-
5
-
5
-
-
-
-
5
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
occurs
x
3
=
18
1+8
9
14
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
18
-
-
14
-
63
-
27
1+4
3
6
4
5
-
5
4
6
3
4
5
-
3
6
4
5
-
-
1+8
-
-
1+4
-
6+3
-
2+7
5
L
O
V
E
-
E
V
O
L
V
E
-
L
O
V
E
-
-
9
-
-
5
-
9
-
9

 

 

14
L
O
V
E
E
V
O
L
V
E
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
6
-
-
+
=
18
1+8
=
9
=
9
=
9
-
-
15
-
-
-
-
15
-
-
-
-
15
-
-
+
=
45
4+5
=
9
=
9
=
9
14
L
O
V
E
E
V
O
L
V
E
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
3
-
4
5
5
4
-
3
4
5
3
-
4
5
+
=
45
4+5
=
9
=
9
=
9
-
12
-
22
5
5
22
-
12
22
5
12
-
22
5
+
=
144
1+4+4
=
9
=
9
=
9
14
L
O
V
E
E
V
O
L
V
E
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
12
15
22
5
5
22
15
12
22
5
12
15
22
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
3
6
4
5
5
4
6
3
4
5
3
6
4
5
+
=
63
6+3
=
9
=
9
=
9
14
L
O
V
E
E
V
O
L
V
E
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
-
-
3
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
4
-
-
4
-
-
4
-
-
-
4
-
-
-
4
occurs
x
4
=
16
1+6
7
-
-
-
-
5
5
-
-
-
-
5
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
-
-
6
-
-
-
-
6
-
-
-
-
6
occurs
x
3
=
18
1+8
9
14
L
O
V
E
E
V
O
L
V
E
L
O
V
E
-
-
18
-
-
14
-
63
-
27
1+4
3
6
4
5
5
4
6
3
4
5
3
6
4
5
-
-
1+8
-
-
1+4
-
6+3
-
2+7
5
L
O
V
E
E
V
O
L
V
E
L
O
V
E
-
-
9
-
-
5
-
9
-
9

 

 

-
LOVE EVOLVE LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
2
L+O
27
9
9
2
V+E
27
9
9
14
LOVE EVOLVE LOVE
189
63
63
1+4
-
1+8+9
6+3
6+3
5
LOVE EVOLVE LOVE
18
9
9
-
-
1+8
-
-
5
LOVE EVOLVE LOVE
9
9
9

 

LOVE EVOLVE LOVE

EVOLVE LOVE EVOLVE

 

-
EVOLVE LOVE EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
2
L+O
27
9
9
2
V+E
27
9
9
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
16
EVOLVE LOVE EVOLVE
216
72
72
1+6
-
2+1+6
7+2
7+2
7
EVOLVE LOVE EVOLVE
9
9
9
-
-
-
-
-
7
EVOLVE LOVE EVOLVE
9
9
9

 

 

-
EVOLVE LOVE LOVE EVOLVE
-
-
-
-
EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
-
EVOLVE
-
-
-
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
-
EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
-
EVOLVE
-
-
-
20
EVOLVE LOVE LOVE EVOLVE
270
90
45
2+0
-
2+7+0
9+0
4+5
2
EVOLVE LOVE LOVE EVOLVE
9
9
9
-
-
-
-
-
2
EVOLVE LOVE LOVE EVOLVE
9
9
9

 

 

-
20
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
-
-
-
15
-
-
-
-
-
15
-
-
-
-
15
-
-
-
-
-
15
-
-
-
+
=
60
6+0
=
6
=
6
=
6
-
20
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
5
4
-
3
4
5
-
3
-
4
5
-
3
-
4
5
-
5
4
-
3
4
5
+
=
66
6+6
=
12
1+2
3
=
3
-
-
5
22
-
12
22
5
-
12
-
22
5
-
12
-
22
5
-
5
22
-
12
22
5
+
=
210
2+1+0
=
3
=
3
=
3
-
20
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
5
22
15
12
22
5
-
12
15
22
5
-
12
15
22
5
-
5
22
15
12
22
5
+
=
270
2+7+0
=
9
=
9
=
9
-
-
5
4
6
3
4
5
-
3
6
4
5
-
3
6
4
5
-
5
4
6
3
4
5
+
=
90
9+0
=
9
=
9
=
9
-
20
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
4
-
-
4
-
-
-
-
4
-
-
-
-
4
-
-
-
4
-
-
4
-
-
-
4
occurs
x
6
=
24
2+4
6
-
-
5
-
-
-
-
5
-
-
-
-
5
-
-
-
-
5
-
5
-
-
-
-
5
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
27
20
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
18
-
-
20
-
90
-
18
2+7
2+0
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+8
-
-
2+0
-
9+0
-
1+8
9
2
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
9
-
-
2
-
9
-
9
-
-
5
4
6
3
4
5
-
3
6
4
5
-
3
6
4
5
-
5
4
6
3
4
5
-
-
-
-
-
-
-
-
-
-
9
2
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
9
-
-
2
-
9
-
9

 

 

20
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
-
-
15
-
-
-
-
-
15
-
-
-
-
15
-
-
-
-
-
15
-
-
-
+
=
60
6+0
=
6
=
6
=
6
20
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
5
4
-
3
4
5
-
3
-
4
5
-
3
-
4
5
-
5
4
-
3
4
5
+
=
66
6+6
=
12
1+2
3
=
3
-
5
22
-
12
22
5
-
12
-
22
5
-
12
-
22
5
-
5
22
-
12
22
5
+
=
210
2+1+0
=
3
=
3
=
3
20
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
5
22
15
12
22
5
-
12
15
22
5
-
12
15
22
5
-
5
22
15
12
22
5
+
=
270
2+7+0
=
9
=
9
=
9
-
5
4
6
3
4
5
-
3
6
4
5
-
3
6
4
5
-
5
4
6
3
4
5
+
=
90
9+0
=
9
=
9
=
9
20
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
4
-
-
4
-
-
-
-
4
-
-
-
-
4
-
-
-
4
-
-
4
-
-
-
4
occurs
x
6
=
24
2+4
6
-
5
-
-
-
-
5
-
-
-
-
5
-
-
-
-
5
-
5
-
-
-
-
5
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
6
-
-
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
20
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
18
-
-
20
-
90
-
18
2+0
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+8
-
-
2+0
-
9+0
-
1+8
2
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
9
-
-
2
-
9
-
9
-
5
4
6
3
4
5
-
3
6
4
5
-
3
6
4
5
-
5
4
6
3
4
5
-
-
-
-
-
-
-
-
-
-
2
E
V
O
L
V
E
-
L
O
V
E
-
L
O
V
E
-
E
V
O
L
V
E
-
-
9
-
-
2
-
9
-
9

 

 

20
E
V
O
L
V
E
L
O
V
E
L
O
V
E
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
-
-
-
6
-
-
-
-
6
-
-
-
+
=
24
2+4
=
6
=
6
=
6
-
-
-
15
-
-
-
-
15
-
-
-
15
-
-
-
-
15
-
-
-
+
=
60
6+0
=
6
=
6
=
6
20
E
V
O
L
V
E
L
O
V
E
L
O
V
E
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
5
4
-
3
4
5
3
-
4
5
3
-
4
5
5
4
-
3
4
5
+
=
66
6+6
=
12
1+2
3
=
3
-
5
22
-
12
22
5
12
-
22
5
12
-
22
5
5
22
-
12
22
5
+
=
210
2+1+0
=
3
=
3
=
3
20
E
V
O
L
V
E
L
O
V
E
L
O
V
E
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
5
22
15
12
22
5
12
15
22
5
12
15
22
5
5
22
15
12
22
5
+
=
270
2+7+0
=
9
=
9
=
9
-
5
4
6
3
4
5
3
6
4
5
3
6
4
5
5
4
6
3
4
5
+
=
90
9+0
=
9
=
9
=
9
20
E
V
O
L
V
E
L
O
V
E
L
O
V
E
E
V
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
-
-
-
3
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
4
-
-
4
-
-
-
4
-
-
-
4
-
-
4
-
-
4
-
-
-
4
occurs
x
6
=
24
2+4
6
-
5
-
-
-
-
5
-
-
-
5
-
-
-
5
5
-
-
-
-
5
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
6
-
-
-
-
6
-
-
-
6
-
-
-
-
6
-
-
-
-
-
6
occurs
x
4
=
24
2+4
6
20
E
V
O
L
V
E
L
O
V
E
L
O
V
E
E
V
O
L
V
E
-
-
18
-
-
20
-
90
-
18
2+0
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1+8
-
-
2+0
-
9+0
-
1+8
2
E
V
O
L
V
E
L
O
V
E
L
O
V
E
E
V
O
L
V
E
-
-
9
-
-
2
-
9
-
9
-
5
4
6
3
4
5
3
6
4
5
3
6
4
5
5
4
6
3
4
5
-
-
-
-
-
-
-
-
-
-
2
E
V
O
L
V
E
L
O
V
E
L
O
V
E
E
V
O
L
V
E
-
-
9
-
-
2
-
9
-
9

 

 

EVOLVE LOVE LOVE EVOLVE

 

-
EVOLVE LOVE LOVE EVOLVE
-
-
-
-
EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
-
EVOLVE
-
-
-
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
-
LOVE
-
-
-
2
L+O
27
9
9
2
V+E
27
9
9
-
LOVE
-
-
-
-
EVOLVE
-
-
-
2
E+V
27
9
9
2
O+L
27
9
9
2
V+E
27
9
9
-
EVOLVE
-
-
-
20
EVOLVE LOVE LOVE EVOLVE
270
90
45
2+0
-
2+7+0
9+0
4+5
2
EVOLVE LOVE LOVE EVOLVE
9
9
9
-
-
-
-
-
2
EVOLVE LOVE LOVE EVOLVE
9
9
9

 

REVOLVER EVOLVER LOVER

 

-
-
-
-
-
REVOLVER
-
-
-
-
-
-
-
1
R
18
9
9
-
-
-
-
2
E+V
27
9
9
-
-
-
-
2
O+L
27
9
9
-
-
-
-
2
V+E
27
9
9
-
-
-
-
1
R
18
9
9
L
=
3
-
8
REVOLVER
117
45
45
-
-
-
-
-
EVOLVER
-
-
-
-
-
-
-
2
E+V
27
9
9
-
-
-
-
2
O+L
27
9
9
-
-
-
-
2
V+E
27
9
9
-
-
-
-
1
R
18
9
9
R
=
9
-
7
EVOLVER
99
36
36
-
-
-
-
-
LOVER
-
-
-
-
5
-
-
2
L+O
27
9
9
-
1
-
-
2
V+E
27
9
9
-
1
-
-
1
R
18
9
9
L
=
3
-
5
LOVER
72
27
27
-
-
-
-
-
-
-
-
-
-
-
15
-
20
288
108
108
-
-
1+5
-
2+0
-
2+7+0
9+0
9+0
-
-
6
-
2
9
9
9

 

REVOLVER EVOLVER LOVER

 

 

-
10
L
O
V
E
S
-
S
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
1
-
1
6
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
-
15
-
-
19
-
19
15
-
-
-
+
=
68
6+8
=
14
1+4
5
=
5
-
10
L
O
V
E
S
-
S
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
4
5
-
-
-
-
3
4
5
+
=
24
2+4
=
6
=
6
=
6
-
-
12
-
22
5
-
-
-
-
12
22
5
+
=
78
7+8
=
15
1+1
6
=
6
-
10
L
O
V
E
S
-
S
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
12
15
22
5
19
-
19
15
12
22
5
+
=
146
1+4+6
=
11
1+1
2
=
2
-
-
3
6
4
5
1
-
1
6
3
4
5
+
=
38
3+8
=
11
1+1
2
=
2
-
10
L
O
V
E
S
-
S
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
Q
-
-
-
4
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
26
10
L
O
V
E
S
-
S
O
L
V
E
-
-
19
-
-
10
-
38
-
20
2+6
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1+9
-
-
1+0
-
3+8
-
2+0
8
1
L
O
V
E
S
-
S
O
L
V
E
-
-
10
-
-
1
-
11
-
2
-
-
3
6
4
5
1
-
1
6
3
4
5
-
-
1+0
-
-
-
-
1+1
-
-
8
1
L
O
V
E
S
-
S
O
L
V
E
-
-
1
-
-
1
-
2
-
2

 

 

10
L
O
V
E
S
-
S
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
1
-
1
6
-
-
-
+
=
14
1+4
=
5
=
5
=
5
-
-
15
-
-
19
-
19
15
-
-
-
+
=
68
6+8
=
14
1+4
5
=
5
10
L
O
V
E
S
-
S
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
3
-
4
5
-
-
-
-
3
4
5
+
=
24
2+4
=
6
=
6
=
6
-
12
-
22
5
-
-
-
-
12
22
5
+
=
78
7+8
=
15
1+1
6
=
6
10
L
O
V
E
S
-
S
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
12
15
22
5
19
-
19
15
12
22
5
+
=
146
1+4+6
=
11
1+1
2
=
2
-
3
6
4
5
1
-
1
6
3
4
5
+
=
38
3+8
=
11
1+1
2
=
2
10
L
O
V
E
S
-
S
O
L
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
3
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
4
-
-
-
-
-
-
4
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
-
-
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
6
-
-
-
-
-
6
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
10
L
O
V
E
S
-
S
O
L
V
E
-
-
19
-
-
10
-
38
-
20
1+0
-
-
-
-
-
-
-
-
-
-
-
-
-
1+9
-
-
1+0
-
3+8
-
2+0
1
L
O
V
E
S
-
S
O
L
V
E
-
-
10
-
-
1
-
11
-
2
-
3
6
4
5
1
-
1
6
3
4
5
-
-
1+0
-
-
-
-
1+1
-
-
1
L
O
V
E
S
-
S
O
L
V
E
-
-
1
-
-
1
-
2
-
2

 

 

6
ALLAHU
55
19
1
5
AKBAR
24
15
6
11
First Total
79
34
7
1+1
Add to Reduce
7+9
3+4
-
2
Second Total
16
7
7
-
Reduce to Deduce
1+6
-
-
2
Essence of Number
7
7
7

 

 

3
GOD
26
17
8
2
IS
28
10
1
5
GREAT
51
24
6
10
Add to Reduce
105
51
15
1+0
Reduce to Deduce
1+0+5
5+1
1+5
1
Essence of Number
6
6
6

 

 

5
ALLAH
34
16
7
3
ALL
25
7
7
2
AH
9
9
9

 

 

3
ALL
25
7
7
3
ARE
24
15
6
2
HE
13
13
4
8
Add to Reduce
62
35
17
-
Reduce to Deduce
6+2
3+5
1+7
8
Essence of Number
8
8
8

 

 

5
ALLAH
34
16
7
5
HALAL
34
16
7
10
First Total
68
32
14
1+0
Add to Reduce
6+8
3+2
1+4
1
Second Total
14
5
5
-
Reduce to Deduce
1+4
-
-
1
Essence of Number
5
5
5

 

 

E
=
5
4
EACH
17
17
8
F
=
6
3
FOR
39
21
3
A
=
1
3
ALL
25
7
7
A
=
1
3
ALL
25
7
7
F
=
6
3
FOR
39
21
3
G
=
7
3
GOD
26
17
8
-
-
26
19
First Total
171
90
36
-
-
2+6
1+9
Add to Reduce
1+7+1
9+0
3+6
-
-
8
10
Second Total
9
9
9
-
-
-
1+0
Reduce to Deduce
-
-
-
-
-
8
1
Essence of Number
9
9
9

 

 

3
YOU
61
16
7
1
I
9
9
9
2
ME
18
18
9
3
THE
33
15
6
4
HERE
36
27
9
2
WE
28
10
1
2
GO
22
13
4
3
EGO
27
18
9
20
Add to Reduce
234
126
54
2+0
Reduce to Deduce
2+3+4
1+2+6
5+4
2
Essence of Number
9
9
9

 

 

3
THE
33
15
6
4
OVER
60
24
6
6
LOADED
41
23
5
3
EGO
27
18
9
16
Add to Reduce
161
80
26
1+6
Reduce to Deduce
1+6+1
8+0
2+6
7
Essence of Number
8
8
8

 

 

8
CHANGING
63
45
9

 

 

7
COMFORT
90
36
9

 

 

5
HEART
52
25
7
3
ART
39
12
3
8
First Total
91
37
10
-
Add to Reduce
9+1
3+7
1+0
8
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
8
Essence of Number
1
1
1

 

 

4
WITH
60
24
6
5
FIRST
72
27
9
7
CONTACT
76
22
4
5
ALIEN
41
23
5
6
ALIENS
51
24
6

 

 

-
FAIRY
-
-
-
1
I
9
9
9
1
R
18
9
9
3
F+A+Y
32
14
5
5
FAIRY
59
32
23
-
-
5+9
3+2
2+3
5
FAIRY
14
5
5
-
-
1+4
-
-
5
FAIRY
5
5
5

 

 

7
ANAELLE
50
23
5

 

 

A
=
1
1
A
1
1
1
F
=
6
5
FAIRY
59
32
5
C
=
3
5
CHILD
36
27
9
A
=
1
3
AND
19
10
1
F
=
6
4
FULL
51
15
6
O
=
6
2
OF
21
12
3
W
=
5
3
WOE
43
16
7
-
-
28
23
Add to Reduce
230
113
32
-
-
10
2+3
Reduce to Deduce
2+3+0
1+1+3
3+2
-
-
1
5
Essence of Number
5
5
5

 

 

1
A
1
1
1
7
FAERIES
63
36
9
5
CHILD
36
27
9
3
AND
19
10
1
4
FULL
51
15
6
2
OF
21
12
3
4
GLOW
57
21
3
26
First Total
248
122
32
2+6
Add to Reduce
2+4+8
1+2+2
3+2
8
Second Total
14
5
5
-
Reduce to Deduce
1+4
-
-
8
Essence of Number
5
5
5

 

 

1
A
1
1
1
5
FAIRY
50
32
5
5
CHILD
36
27
9
3
AND
19
10
1
4
FULL
51
15
6
2
OF
21
12
3
4
GLOW
57
21
3
24
First Total
235
118
28
2+4
Add to Reduce
2+3+5
1+1+8
2+8
6
Second Total
10
10
10
-
Reduce to Deduce
1+0
1+0
1+0
6
Essence of Number
1
1
1

 

 

3
LIVE
48
21
3
3
EVIL
48
21
3
4
VEIL
48
21
3
-
-
-
-
-
-
-
-
-
-
5
BURKA
53
17
8
5
NIQAB
43
25
7

 

 

T
=
2
-
3
THE
33
15
6
H
=
8
-
9
HASTENING
97
43
7
W
=
5
-
5
WHILE
57
30
3
S
-
15
4
17
First Total
187
88
16
-
-
1+5
-
1+7
Add to Reduce
1+8+7
8+8
1+6
-
-
6
-
8
Second Total
16
16
7
-
-
-
-
-
Reduce to Deduce
1+6
1+6
-
-
-
6
-
8
Essence of Number
7
7
7

 

 

-
15
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
8
-
1
-
-
5
9
5
-
-
-
8
9
-
-
+
=
53
5+3
=
8
=
8
=
8
-
-
-
8
-
-
8
-
19
-
-
14
9
14
-
-
-
8
9
-
-
+
=
89
8+9
=
17
1+7
8
=
8
8
15
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
1
-
2
5
-
-
-
7
-
5
-
-
3
5
+
=
35
3+5
=
8
=
8
=
8
-
-
20
-
5
-
-
1
-
20
5
-
-
-
7
-
23
-
-
12
5
+
=
98
9+8
=
17
1+7
8
=
8
-
15
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
8
1
19
20
5
14
9
14
7
-
23
8
9
12
5
+
=
187
1+8+7
=
16
1+6
7
=
7
-
-
2
8
5
-
8
1
1
2
5
5
9
5
7
-
5
8
9
3
5
+
=
88
8+8
=
16
1+6
7
=
7
-
15
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
``-
2
-
-
-`
-
-
-
2
-
-
-
-
-
-`
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
5
5
-
5
-
-
5
-
-
-
5
-
-
5
occurs
x
6
=
30
3+0
3`
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
10
15
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
35
-
-
15
-
88
-
34
1+0
1+5
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
3+5
-
-
1+5
-
8+8
-
3+4
1
6
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
8
-
-
6
-
16
-
7
-
-
2
8
5
-
8
1
1
2
5
5
9
5
7
-
5
8
9
3
5
-
-
-
-
-
-
-
1+6
-
-
1
6
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
8
-
-
6
-
7
-
7

 

 

15
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
8
-
1
-
-
5
9
5
-
-
-
8
9
-
-
+
=
53
5+3
=
8
=
8
=
8
-
-
8
-
-
8
-
19
-
-
14
9
14
-
-
-
8
9
-
-
+
=
89
8+9
=
17
1+7
8
=
8
15
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
1
-
2
5
-
-
-
7
-
5
-
-
3
5
+
=
35
3+5
=
8
=
8
=
8
-
20
-
5
-
-
1
-
20
5
-
-
-
7
-
23
-
-
12
5
+
=
98
9+8
=
17
1+7
8
=
8
15
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
8
1
19
20
5
14
9
14
7
-
23
8
9
12
5
+
=
187
1+8+7
=
16
1+6
7
=
7
-
2
8
5
-
8
1
1
2
5
5
9
5
7
-
5
8
9
3
5
+
=
88
8+8
=
16
1+6
7
=
7
15
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
``-
2
-
-
-`
-
-
-
2
-
-
-
-
-
-`
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
5
-
-
-
-
-
5
5
-
5
-
-
5
-
-
-
5
-
-
5
occurs
x
6
=
30
3+0
3`
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
3
=
24
2+4
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
15
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
35
-
-
15
-
88
-
34
1+5
-
-
5
-
-
-
-
-
5
5
-
5
-
-
5
-
-
-
5
-
-
3+5
-
-
1+5
-
8+8
-
3+4
6
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
8
-
-
6
-
16
-
7
-
2
8
5
-
8
1
1
2
5
5
9
5
7
-
5
8
9
3
5
-
-
-
-
-
-
-
1+6
-
-
6
T
H
E
-
H
A
S
T
E
N
I
N
G
-
W
H
I
L
E
-
-
8
-
-
6
-
7
-
7

 

 

15
T
H
E
H
A
S
T
E
N
I
N
G
W
H
I
L
E
-
-
-
-
-
-
-
-
-
-
-
-
8
-
8
-
1
-
-
5
9
5
-
-
8
9
-
-
+
=
53
5+3
=
8
=
8
=
8
-
-
8
-
8
-
19
-
-
14
9
14
-
-
8
9
-
-
+
=
89
8+9
=
17
1+7
8
=
8
15
T
H
E
H
A
S
T
E
N
I
N
G
W
H
I
L
E
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
1
-
2
5
-
-
-
7
5
-
-
3
5
+
=
35
3+5
=
8
=
8
=
8
-
20
-
5
-
1
-
20
5
-
-
-
7
23
-
-
12
5
+
=
98
9+8
=
17
1+7
8
=
8
15
T
H
E
H
A
S
T
E
N
I
N
G
W
H
I
L
E
-
-
-
-
-
--
-
-
-
-
-
20
8
5
8
1
19
20
5
14
9
14
7
23
8
9
12
5
+
=
187
1+8+7
=
16
1+6
7
=
7
-
2
8
5
8
1
1
2
5
5
9
5
7
5
8
9
3
5
+
=
88
8+8
=
16
1+6
7
=
7
15
T
H
E
H
A
S
T
E
N
I
N
G
W
H
I
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
``-
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
5
-
-
-
-
5
5
-
5
-
5
-
-
-
5
-
-
5
occurs
x
6
=
30
3+0
3`
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
3
=
24
2+4
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
15
T
H
E
H
A
S
T
E
N
I
N
G
W
H
I
L
E
-
-
35
-
-
15
-
88
-
34
1+5
-
-
5
-
-
-
-
5
5
-
5
-
5
-
-
-
5
-
-
3+5
-
-
1+5
-
8+8
-
3+4
6
T
H
E
H
A
S
T
E
N
I
N
G
W
H
I
L
E
-
-
8
-
-
6
-
16
-
7
-
2
8
5
8
1
1
2
5
5
9
5
7
5
8
9
3
5
-
-
-
-
-
-
-
1+6
-
-
6
T
H
E
H
A
S
T
E
N
I
N
G
W
H
I
L
E
-
-
8
-
-
6
-
7
-
7

 

 

6
FOLLOW
83
29
2
7
FOLLOWS
102
30
3
9
FOLLOWING
113
50
5
8
FOLLOWED
92
38
2

 

 

-
PHI
-
-
-
-
P
16
7
7
-
H
8
8
8
-
I
9
9
9
3
PHI
33
24
24
-
-
3+3
2+4
2+4
3
PHI
6
6
6

 

►Golden ratio - Wikipedia, the free encyclopedia Mark Barr (20th century) suggests the Greek letter phi (φ), the initial ...
en.wikipedia.org/wiki/Golden_ratio -

Show more results from wikipedia.orgPhi: 1.618. The best source to the golden section, golden mean ... The best information on the Golden Section, Divine Proportion, Fibonacci series and phi. Explore its application to art, design, life, beauty, mathematics, ...
www.goldennumber.net/ -

the golden ratio = 1.61803399
More about calculator.

Search ResultsPhi - Wikipedia, the free encyclopediaPhi (uppercase Φ, lowercase φ or math symbol ϕ), pronounced /ˈfaɪ/ or sometimes /ˈfiː/ in English, and [ˈfi] in modern Greek, is the 21st letter of the ...
en.wikipedia.org/wiki/Phi -

PhiFrom Wikipedia, the free encyclopediaJump to: navigation, search
For other uses, see Phi (disambiguation).

Greek alphabet
Αα Alpha Νν Nu
Ββ Beta Ξξ Xi
Γγ Gamma Οο Omicron
Δδ Delta Ππ Pi
Εε Epsilon Ρρ Rho
Ζζ Zeta Σσς Sigma
Ηη Eta Ττ Tau
Θθ Theta Υυ Upsilon
Ιι Iota Φφ Phi
Κκ Kappa Χχ Chi
Λλ Lambda Ψψ Psi
Μμ Mu Ωω Omega
Other characters
Digamma Stigma
Heta San
Qoppa Sampi
Greek diacritics

Phi (uppercase Φ, lowercase φ or math symbol ϕ), pronounced /ˈfaɪ/ or sometimes /ˈfiː/ in English,[1] and [ˈfi] in modern Greek, is the 21st letter of the Greek alphabet. In modern Greek, it represents [f], a voiceless labiodental fricative. In Ancient Greek it represented [pʰ], an aspirated voiceless bilabial plosive (from which English ultimately inherits the spelling "ph" in words derived from Greek). In the system of Greek numerals it has a value of 500 (φʹ) or 500,000 (͵φ). The Cyrillic letter Ef (Ф, ф) arose from Φ.

Contents [hide]
1 Use as a symbol
2 Computing
3 See also
4 References

Use as a symbolThe lower-case letter (or often its variant, ) is often used to represent the following:

The golden ratio in mathematics, art, and architecture.
Euler's totient function φ(n) in number theory; also called Euler's phi function.
In algebra, group or ring homomorphisms
In probability theory, ϕ(x) = (2π)−½e−x2/2 is the probability density function of the normal distribution.
In probability theory, φX(t) = E[ eitX ] is the characteristic function of a random variable X.
An angle, typically the second angle mentioned, after θ (theta). Especially:
The argument of a complex number.
The phase of a wave in signal processing.
In spherical coordinates, mathematicians usually refer to phi as the polar angle (from the z-axis). The convention in physics is to use phi as the azimuthal angle (from the x-axis).
One of the dihedral angles in the backbones of proteins.
Internal or effective angle of friction.
Electric potential in physics.
The work function in electronics.
A shorthand representation for an aromatic functional group in organic chemistry.
The fugacity coefficient in thermodynamics.
The ratio of free energy destabilizations of protein mutants in phi value analysis.
In cartography and navigation, latitude.
In combustion engineering, equivalence ratio. The ratio between the actual fuel air ratio to the stoichiometric fuel air ratio.
A sentence in first-order logic.
Porosity in geology and hydrology.
Strength (or resistance) reduction factor in structural engineering, used to account for statistical variabilities in materials and construction methods.
The symbol for a voiceless bilabial fricative in the International Phonetic Alphabet (using the straight line variant character)
In economics, this is usually an additive term.[clarification needed]
In flight dynamics, the roll angle.
The upper-case letter Φ is used as a symbol for:

The golden ratio conjugate −0.618... in mathematics.
The magnetic flux and electric flux in physics, with subscripts distinguishing the two.
The cumulative distribution function of the normal distribution in mathematics and statistics.
Philosophy.[why?]
The number of phases in a power system in electrical engineering, for example 1Φ for single phase, 3Φ for three phase.
A common symbol for the parametrization of a surface in vector calculus.
In Lacanian algebra, Φ stands for the imaginary phallus and also represents phallic signification. -Φ stands in for castration.[2]
The diameter symbol in engineering, ⌀, is often incorrectly referred to as "phi". This symbol is used to indicate the diameter of a circular section, for example "⌀14", means the diameter of the circle is 14 units.

 

 

-
PHI
-
-
-
-
P
16
7
7
-
H
8
8
8
-
I
9
9
9
3
PHI
33
24
24
-
-
3+3
2+4
2+4
3
PHI
6
6
6

 

 

-
3
P
H
1
-
-
-
-
-
-
-
-
-
-
-
8
9
+
=
17
1+7
=
8
=
8
-
-
-
8
9
+
=
17
1+7
=
8
=
8
-
3
P
H
1
-
-
-
-
-
-
-
-
-
-
7
-
-
+
=
7
-
=
7
=
7
-
`-
16
-
-
+
=
16
1+6
=
7
=
7
-
3
P
H
1
-
-
-
-
-
-
-
-
-
-
16
8
9
+
=
33
3+3
=
6
=
6
-
-
7
8
9
+
=
24
2+4
=
6
=
6
-
3
P
H
I
-T
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
ONE
1
-
-
-
2
-
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
-
6
SIX
6
-
-
-
-
--
7
-
-
-
-
7
occurs
x
1
=
7
-
-
-
8
-
-
-
8
occurs
x
1
=
8
-
-
-
-
9
-
-
9
occurs
x
1
=
9
21
3
P
H
I
-
-
24
-
-
3
-
24
2+1
-
-
-
9
-
-
2+4
-
-
-
-
2+4
3
3
P
H
I
-
-
6
-
-
3
-
6
-
-
7
8
9
-T
-
-
-
-
-
-
-
3
3
P
H
I
-
-
6
-
-
3
-
6

 

 

-
3
P
H
1
-
-
-
-
-
-
-
-
-
-
-
8
9
+
=
17
1+7
=
8
=
8
-
-
-
8
9
+
=
17
1+7
=
8
=
8
-
3
P
H
1
-
-
-
-
-
-
-
-
-
-
7
-
-
+
=
7
-
=
7
=
7
-
`-
16
-
-
+
=
16
1+6
=
7
=
7
-
3
P
H
1
-
-
-
-
-
-
-
-
-
-
16
8
9
+
=
33
3+3
=
6
=
6
-
-
7
8
9
+
=
24
2+4
=
6
=
6
-
3
P
H
I
-T
-
-
-
-
-
-
-
-
--
7
-
-
-
-
7
occurs
x
1
=
7
-
-
-
8
-
-
-
8
occurs
x
1
=
8
-
-
-
-
9
-
-
9
occurs
x
1
=
9
21
3
P
H
I
-
-
24
-
-
3
-
24
2+1
-
-
-
9
-
-
2+4
-
-
-
-
2+4
3
3
P
H
I
-
-
6
-
-
3
-
6
-
-
7
8
9
-T
-
-
-
-
-
-
-
3
3
P
H
I
-
-
6
-
-
3
-
6

 

 

-
PHI
-
-
-
-
P
16
7
7
-
H
8
8
8
-
I
9
9
9
3
PHI
33
24
24
-
-
3+3
2+4
2+4
3
PHI
6
6
6

 

 

Pi - Wikipedia, the free encyclopediaπ (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in the Euclidean plane; ...

Fundamentals - History - Open questions - Use in mathematics and science
en.wikipedia.org/wiki/Pi -

 

PiFrom Wikipedia, the free encyclopediaJump to: navigation, search
This article is about the number. For the Greek letter, see Pi (letter). For other uses, see Pi (disambiguation).

Mosaic depicting π at the entrance to the math building at Technische Universität BerlinPart of a series of articles on
the mathematical constant π

Uses
Area of disk · Circumference
Use in other formulae
Properties
Irrationality · Transcendence
Less than 22/7
Value
Approximations · Memorization
People
Archimedes · Zu Chongzhi
Madhava of Sangamagrama
William Jones · John Machin
John Wrench
History
Chronology · Book
In culture
Legislation · Holiday
Related topics
Squaring the circle · Basel problem
Other topics related to π
v · d · e

π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in the Euclidean plane; this is the same value as the ratio of a circle's area to the square of its radius. It is approximately equal to 3.14159265 in the usual decimal notation. Many formulae from mathematics, science, and engineering involve π, which makes it one of the most important mathematical constants.[1]

π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics. Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture.

Probably because of the simplicity of its definition, the concept of π has become entrenched in popular culture to a degree far greater than almost any other mathematical construct.[2] It is, perhaps, the most common ground between mathematicians and non-mathematicians.[3] Reports on the latest, most-precise calculation of π (and related stunts) are common news items.[4][5][6] The current record for the decimal expansion of π, if verified, stands at 5 trillion digits.[7]

The Greek letter π, often spelled out pi in text, was first adopted for the number as an abbreviation of the Greek word for perimeter "περίμετρος" (or as an abbreviation for "perimeter/diameter") by William Jones in 1706. The constant is also known as Archimedes' Constant, after Archimedes of Syracuse who provided an approximation of the number, although this name for the constant is uncommon in modern English-speaking contexts.

Contents [hide]
1 Fundamentals
1.1 The letter π
1.2 Geometric definition
1.3 Irrationality and transcendence
1.4 Decimal representation
1.5 Estimating π
2 History
2.1 Antiquity
2.2 Second millennium AD
2.3 Computation in the computer age
2.4 Pi and continued fraction
2.5 Memorizing digits
3 Open questions
4 Use in mathematics and science
4.1 Geometry and trigonometry
4.2 Complex numbers and calculus
4.3 Physics
4.4 Probability and statistics
4.5 Geomorphology and chaos theory
5 In popular culture
6 See also
7 References
8 External links

FundamentalsThe letter πMain article: pi (letter)

Lower-case π is used to symbolize the constantThe name of the Greek letter π is pi.[8] The name pi is commonly used as an alternative to using the Greek letter. As a mathematical symbol, the Greek letter is not capitalized (Π) even at the beginning of a sentence, and instead the lower case (π) is used at the beginning of a sentence. When referring to this constant, the symbol π is always pronounced "pie" in English, which is the conventional English pronunciation of the Greek letter. The constant is named "π" because "π" is the first letter of the Greek word περίμετρος (perimeter), probably referring to its use in the formula perimeter/diameter which is constant for all circles, the word "perimeter" being synonymous here with "circumference."[9] William Jones was the first to use the Greek letter in this way, in 1706,[10] and it was later popularized by Leonhard Euler in 1737.[11][12] William Jones wrote:

There are various other ways of finding the Lengths or Areas of particular Curve Lines, or Planes, which may very much facilitate the Practice; as for instance, in the Circle, the Diameter is to the Circumference as 1 to ... 3.14159, &c. = π[13]

The capital letter pi (Π) has a completely different mathematical meaning; it is used for expressing products (notice that the word "product" begins with the letter "p" just like "perimeter/diameter" does). It can also refer to the osmotic pressure of a solution.

Geometric definitionIn Euclidean plane geometry, π is defined as the ratio of a circle's circumference C to its diameter d:[9]

The ratio C/d is constant, regardless of a circle's size. For example, if a circle has twice the diameter d of another circle it will also have twice the circumference C, preserving the ratio C/d.

Alternatively π can be defined as the ratio of a circle's area A to the area of a square whose side is equal to the radius r of the circle:[9][14]

These definitions depend on results of Euclidean geometry, such as the fact that all circles are similar, and the fact that the right-hand-sides of these two equations are equal to each other (i.e. the area of a disk is Cr/2). These two geometric definitions can be considered a problem when π occurs in areas of mathematics that otherwise do not involve geometry. For this reason, mathematicians often prefer to define π without reference to geometry, instead selecting one of its analytic properties as a definition. A common choice is to define π as twice the smallest positive x for which the trigonometric function cos(x) equals zero.[15

(Diagrams omitted)

Irrationality and transcendenceMain article: Proof that π is irrational
π is an irrational number, meaning that it cannot be written as the ratio of two integers. π is also a transcendental number, meaning that there is no polynomial with rational coefficients for which π is a root.[16] An important consequence of the transcendence of π is the fact that it is not constructible. Because the coordinates of all points that can be constructed with compass and straightedge are constructible numbers, it is impossible to square the circle: that is, it is impossible to construct, using compass and straightedge alone, a square whose area is equal to the area of a given circle.[17] This is historically significant, for squaring a circle is one of the easily understood elementary geometry problems left to us from antiquity; many amateurs in modern times have attempted to solve each of these problems, and their efforts are sometimes ingenious, but in this case, doomed to failure: a fact not always understood by the amateur involved.[18][19]

Decimal representationSee also: Numerical approximations of π
The decimal representation of π truncated to 50 decimal places is:[20]

π = 3.14159265358979323846264338327950288419716939937510...
Various online web sites provide π to many more digits.[21] While the decimal representation of π has been computed to more than a trillion (1012) digits,[22] elementary applications, such as estimating the circumference of a circle, will rarely require more than a dozen decimal places. For example, the decimal representation of π truncated to 11 decimal places is good enough to estimate the circumference of any circle that fits inside the Earth with an error of less than one millimetre, and the decimal representation of π truncated to 39 decimal places is sufficient to estimate the circumference of any circle that fits in the observable universe with precision comparable to the radius of a hydrogen atom.[23][24]

Because π is an irrational number, its decimal representation does not repeat, and therefore does not terminate. This sequence of non-repeating digits has fascinated mathematicians and laymen alike, and much effort over the last few centuries has been put into computing ever more of these digits and investigating π's properties.[25] Despite much analytical work, and supercomputer calculations that have determined over 1 trillion digits of the decimal representation of π, no simple base-10 pattern in the digits has ever been found.[26] Digits of the decimal representation of π are available on many web pages, and there is software for calculating the decimal representation of π to billions of digits on any personal computer.

Estimating πMain article: Numerical approximations of π

Number system Approximation of π
Binary 11.00100100001111110110...[27]
Octal 3.11037552421026430215...
Decimal 3.14159265358979323846264338327950288...
Hexadecimal 3.243F6A8885A308D31319...[28]
Rational approximations 3, 22⁄7, 333⁄106, 355⁄113, 103993/33102, ...[29]
(listed in order of increasing accuracy)

Continued fraction [3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1...][30]
(This fraction is not periodic. Shown in linear notation)

3.1415926535 8979323846 2643383279 5028841971 6939937510
5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 3809525720 1065485863 2788659361 5338182796 8230301952 0353018529 6899577362 2599413891 2497217752 8347913151 5574857242 4541506959

An estimate of π accurate to 1120 decimal digits was obtained using a gear-driven calculator in 1948, by John Wrench and Levi Smith. This was the most accurate estimate of π before electronic computers came into use.[31]

The earliest numerical approximation of π is almost certainly the value 3.[32] In cases where little precision is required, it may be an acceptable substitute. That 3 is an underestimate follows from the fact that it is the ratio of the perimeter of an inscribed regular hexagon to the diameter of the circle.

π can be empirically estimated by drawing a large circle, then measuring its diameter and circumference and dividing the circumference by the diameter. Another geometry-based approach, attributed to Archimedes,[33] is to calculate the perimeter, Pn , of a regular polygon with n sides circumscribed around a circle with diameter d. Then compute the limit of a sequence as n increases to infinity:

This limit converges because the more sides the polygon has, the closer the ratio approaches π. Archimedes determined the accuracy of this approach by comparing the perimeter of the circumscribed polygon with the perimeter of a regular polygon with the same number of sides inscribed inside the circle. Using a polygon with 96 sides, he computed the fractional range:[34]

π can also be calculated using purely mathematical methods. Due to the transcendental nature of π, there are no closed form expressions for the number in terms of algebraic numbers and functions.[16] Formulas for calculating π using elementary arithmetic typically include series or summation notation (such as "..."), which indicates that the formula is really a formula for an infinite sequence of approximations to π.[35] The more terms included in a calculation, the closer to π the result will get.

Most formulae used for calculating the value of π have desirable mathematical properties, but are difficult to understand without a background in trigonometry and calculus. However, some are quite simple, such as this form of the Gregory-Leibniz series:[36]

 

 

-
PI
-
-
-
-
P
16
7
7
-
I
9
9
9
2
PI
25
16
16
-
-
2+5
1+6
1+6
2
PI
7
7
7

 

 

-
2
P
1
-
-
-
-
-
-
-
-
-
-
-
9
+
=
9
1+7
=
8
=
8
-
-
-
9
+
=
9
1+7
=
8
=
8
-
2
P
1
-
-
-
-
-
-
-
-
-
-
7
-
+
=
7
-
=
7
=
7
-
-
16
-
+
=
16
1+6
=
7
=
7
-
2
P
1
-
-
-
-
-
-
-
-
-
-
16
9
+
=
25
2+5
=
7
=
7
-
-
7
9
+
=
16
1+6
=
7
=
7
-
2
P
I
-T
-
-
-
-
-
-
-
1
-
-
-
-
-
1
ONE
1
-
-
-
2
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
29
2
P
I
-
-
16
-
-
2
-
16
2+9
-
-
9
-
-
2+4
-
-
-
-
1+6
11
2
P
I
-
-
6
-
-
2
-
7
1+1
-
7
9
-T
-
-
-
-
-
-
-
2
2
P
I
-
-
6
-
-
2
-
7

 

 

-
2
P
1
-
-
-
-
-
-
-
-
-
-
-
9
+
=
9
1+7
=
8
=
8
-
-
-
9
+
=
9
1+7
=
8
=
8
-
2
P
1
-
-
-
-
-
-
-
-
-
-
7
-
+
=
7
-
=
7
=
7
-
-
16
-
+
=
16
1+6
=
7
=
7
-
2
P
1
-
-
-
-
-
-
-
-
-
-
16
9
+
=
25
2+5
=
7
=
7
-
-
7
9
+
=
16
1+6
=
7
=
7
-
2
P
I
-T
-
-
-
-
-
-
-
1
-
-
-
-
-
1
ONE
1
-
-
-
2
-
-
-
-
-
2
TWO
2
-
-
-
3
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
5
FIVE
5
-
-
-
6
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
29
2
P
I
-
-
16
-
-
2
-
16
2+9
-
-
9
-
-
2+4
-
-
-
-
1+6
11
2
P
I
-
-
6
-
-
2
-
7
1+1
-
7
9
-T
-
-
-
-
-
-
-
2
2
P
I
-
-
6
-
-
2
-
7

 

 

-
2
P
1
-
-
-
-
-
-
-
-
-
-
-
9
+
=
9
1+7
=
8
=
8
-
-
-
9
+
=
9
1+7
=
8
=
8
-
2
P
1
-
-
-
-
-
-
-
-
-
-
7
-
+
=
7
-
=
7
=
7
-
-
16
-
+
=
16
1+6
=
7
=
7
-
2
P
1
-
-
-
-
-
-
-
-
-
-
16
9
+
=
25
2+5
=
7
=
7
-
-
7
9
+
=
16
1+6
=
7
=
7
-
2
P
I
-T
-
-
-
-
-
-
-
-
-
7
-
-
-
7
occurs
x
1
=
7
-
-
-
9
-
-
9
occurs
x
1
=
9
29
2
P
I
-
-
16
-
-
2
-
16
2+9
-
-
9
-
-
2+4
-
-
-
-
1+6
11
2
P
I
-
-
6
-
-
2
-
7
1+1
-
7
9
-T
-
-
-
-
-
-
-
2
2
P
I
-
-
6
-
-
2
-
7

 

 

-
ELECTRICITY
-
-
-
5
ELECT
45
18
9
1
R
18
9
9
1
I
9
9
9
1
C
3
3
3
1
I
9
9
9
2
T+Y
45
9
9
11
ELECTRICITY
129
57
48
1+1
-
1+2+9
5+7
4+8
2
ELECTRICITY
12
12
12
-
-
1+2
1+2
1+2
2
ELECTRICITY
3
3
3

 

 

-
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
+
=
18
1+8
=
9
=
9
=
9
-
-
-
-
-
-
-
-
9
-
9
-
-
+
=
18
1+8
=
9
=
9
=
9
-
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
3
-
2
7
+
=
39
3+9
=
12
1+2
3
=
3
-
-
5
12
5
3
20
18
-
3
-
20
25
+
=
111
1+1+1
=
3
=
3
=
3
-
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
5
12
5
3
20
18
9
3
9
20
25
+
=
129
1+2+9
=
12
1+2
3
=
3
-
-
5
3
5
3
2
9
9
3
9
2
7
+
=
57
5+7
=
12
1+2
3
=
3
-
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
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1
-
-
-
-
-
-
-
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-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
3
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
19
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
26
-
-
11
-
57
-
30
1+9
1+1
-
-
-
-
-
9
9
-
9
-
-
-
-
2+6
-
-
1+1
-
5+7
-
3+0
10
2
E
L
E
C
T
R
I
C
I
T
Y
-
-
8
-
-
2
-
12
-
3
1+0
-
5
3
5
3
2
9
9
3
9
2
7
-
-
-
-
-
-
-
1+2
-
-
1
2
E
L
E
C
T
R
I
C
I
T
Y
-
-
8
-
-
2
-
3
-
3

 

 

11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
+
=
18
1+8
=
9
=
9
=
9
-
-
-
-
-
-
-
9
-
9
-
-
+
=
18
1+8
=
9
=
9
=
9
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
3
-
2
7
+
=
39
3+9
=
12
1+2
3
=
3
-
5
12
5
3
20
18
-
3
-
20
25
+
=
111
1+1+1
=
3
=
3
=
3
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
5
12
5
3
20
18
9
3
9
20
25
+
=
129
1+2+9
=
12
1+2
3
=
3
-
5
3
5
3
2
9
9
3
9
2
7
+
=
57
5+7
=
12
1+2
3
=
3
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
-
2
occurs
x
2
=
4
=
4
-
-
3
-
3
-
-
-
3
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
5
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
9
9
-
9
-
-
-
-
9
occurs
x
3
=
27
2+7
9
11
E
L
E
C
T
R
I
C
I
T
Y
-
-
26
-
-
11
-
57
-
30
1+1
-
-
-
-
-
9
9
-
9
-
-
-
-
2+6
-
-
1+1
-
5+7
-
3+0
2
E
L
E
C
T
R
I
C
I
T
Y
-
-
8
-
-
2
-
12
-
3
-
5
3
5
3
2
9
9
3
9
2
7
-
-
-
-
-
-
-
1+2
-
-
2
E
L
E
C
T
R
I
C
I
T
Y
-
-
8
-
-
2
-
3
-
3

 

 

-
ELECTRIC
-
-
-
5
ELECT
75
18
9
1
R
18
9
9
1
I
9
9
9
1
C
3
3
3
8
ELECTRIC
75
39
30
-
-
7+5
3+9
3+0
8
ELECTRIC
12
12
3
-
-
1+2
1+2
-
8
ELECTRIC
3
3
3

 

ELECTRIC ET CIRCLE ET ELECTRIC

 

-
-
-
-
-
ELECTRIC
-
-
-
E
-
5
-
1
E
5
5
5
T
-
2
-
1
T
20
2
2
C
-
3
-
1
C
3
3
3
I
-
9
-
1
I
9
9
9
R
-
9
-
1
R
18
9
9
C
=
3
-
1
C
3
3
3
L
=
3
-
1
L
12
3
3
E
=
5
-
1
E
5
5
5
-
-
39
-
8
ELECTRIC
75
39
39
-
-
3+9
-
-
-
7+5
3+9
3+9
-
-
12
-
8
ELECTRIC
12
12
12
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
3
-
8
ELECTRIC
3
3
3

 

 

-
-
-
-
-
ELECTRIC
-
-
-
E
-
5
-
1
E+T
25
7
7
C
-
3
-
1
C
3
3
3
I
-
9
-
1
I
9
9
9
R
-
9
-
1
R
18
9
9
C
=
3
-
1
C
3
3
3
L
=
3
-
1
L
12
3
3
E
=
5
-
1
E
5
5
5
-
-
39
3
8
ELECTRIC
75
39
39
-
-
3+9
-
-
-
7+5
3+9
3+9
-
-
12
3
8
ELECTRIC
12
12
12
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
3
3
8
ELECTRIC
3
3
3

 

 

-
-
-
-
-
ELECTRIC
-
-
-
E
-
5
-
1
E
5
5
5
L
-
2
-
1
L
12
3
3
E
-
3
-
1
E
5
5
5
C
-
9
-
1
C
3
3
3
T
-
9
-
1
T
20
2
2
R
=
3
-
1
R
18
9
9
I
=
3
-
1
I
9
9
9
C
=
5
-
1
C
3
3
3
-
-
39
-
8
ELECTRIC
75
39
39
-
-
3+9
-
-
-
7+5
3+9
3+9
-
-
12
-
8
ELECTRIC
12
12
12
-
-
1+2
-
-
-
1+2
1+2
1+2
-
-
3
-
8
ELECTRIC
3
3
3

 

 

-
8
E
L
E
C
T
R
I
C
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
9
-
+
=
9
-
=
9
=
9
=
9
-
8
E
L
E
C
T
R
I
C
-
-
-
-
-
-
-
-
-
-
-
-
5
3
5
3
2
9
-
3
+
=
30
3+9
=
12
1+2
3
=
3
-
-
5
12
5
3
20
18
-
3
+
=
66
1+1+1
=
3
=
3
=
3
-
8
E
L
E
C
T
R
I
C
-
-
-
-
-
-
-
-
-
-
-
-
5
12
5
3
20
18
9
3
+
=
75
7+5
=
12
1+2
3
=
3
-
-
5
3
5
3
2
9
9
3
+
=
39
3+9
=
12
1+2
3
=
3
-
8
E
L
E
C
T
R
I
C
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
3
-
3
-
-
-
3
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
5
-
5
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
9
occurs
x
2
=
18
1+8
9
26
8
E
L
E
C
T
R
I
C
-
-
19
-
-
8
-
39
-
21
2+6
-
-
-
-
-
-
9
9
-
-
-
1+9
-
-
-
-
3+9
-
2+1
8
8
E
L
E
C
T
R
I
C
-
-
10
-
-
8
-
12
-
3
-
-
5
3
5
3
2
9
9
3
-
-
1+0
-
-
-
-
-
-
-
8
8
E
L
E
C
T
R
I
C
-
-
1
-
-
8
-
3
-
3

 

 

ELECTRIC = ET CIRCLE = ELECTRIC

 

E
-
5
-
-
ELECTRIC
-
-
-
-
-
-
-
1
E+T
25
7
7
-
-
-
-
1
C
3
3
3
-
-
-
-
1
I
9
9
9
-
-
-
-
1
R
18
9
9
-
-
-
-
1
C
3
3
3
-
-
-
-
1
L
12
3
3
-
-
-
-
1
E
5
5
5
E
-
5
-
8
ELECTRIC
75
39
39
-
-
-
-
-
-
7+5
3+9
3+9
E
-
5
-
8
ELECTRIC
12
12
12
-
-
-
-
-
-
1+2
1+2
1+2
E
-
5
-
8
ELECTRIC
3
3
3

 

ELECTRIC = ET CIRCLE = ELECTRIC

 

C
=
3
-
CIRCLE
-
-
-
-
-
-
1
C
3
3
3
-
-
-
1
I
9
9
9
-
-
-
1
R
18
9
9
-
-
-
1
C
3
3
3
-
-
-
1
L
12
3
3
-
-
-
1
E
5
5
5
C
=
3
6
CIRCLE
50
32
32
-
-
-
-
-
5+0
3+2
3+2
C
=
3
6
CIRCLE
5
5
5

 

 

-
-
-
-
CIRCLE
-
-
-
-
-
-
5
CIRCL
45
27
9
-
-
-
1
E
5
5
5
C
=
3
6
CIRCLE
50
32
32
-
-
-
-
-
5+0
3+2
3+2
C
=
3
6
CIRCLE
5
5
5

 

 

-
6
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
9
-
-
-
-
+
=
9
-
=
9
=
9
=
9
-
6
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
5
+
=
23
2+3
=
5
=
5
=
5
-
-
3
-
18
3
12
5
+
=
32
3+2
=
5
=
5
=
5
-
6
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
12
5
+
=
50
5+0
=
5
=
5
=
5
-
-
3
9
9
3
3
5
+
=
32
3+2
=
5
=
5
=
5
-
6
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
4
FOUR
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
28
6
C
I
R
C
L
E
-
-
17
-
-
6
-
32
-
23
2+8
-
-
9
9
-
-
-
-
-
1+7
-
-
-
-
3+2
-
2+3
10
6
C
I
R
C
L
E
-
-
8
-
-
6
-
5
-
5
1+0
-
3
9
9
3
3
5
-
-
-
-
-
-
-
-
-
-
1
6
C
I
R
C
L
E
-
-
8
-
-
6
-
5
-
5

 

 

6
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
9
-
-
-
-
+
=
9
-
=
9
=
9
=
9
6
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
5
+
=
23
2+3
=
5
=
5
=
5
-
3
-
18
3
12
5
+
=
32
3+2
=
5
=
5
=
5
6
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
12
5
+
=
50
5+0
=
5
=
5
=
5
-
3
9
9
3
3
5
+
=
32
3+2
=
5
=
5
=
5
6
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
9
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
6
C
I
R
C
L
E
-
-
17
-
-
6
-
32
-
23
-
-
9
9
-
-
-
-
-
1+7
-
-
-
-
3+2
-
2+3
6
C
I
R
C
L
E
-
-
8
-
-
6
-
5
-
5
-
3
9
9
3
3
5
-
-
-
-
-
-
-
-
-
-
6
C
I
R
C
L
E
-
-
8
-
-
6
-
5
-
5

 

 

-
8
C
I
R
C
U
L
A
R
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
+
=
9
=
9
-
=
8
=
8
-
-
-
9
-
-
-
-
-
-
+
=
9
=
9
-
=
8
=
8
-
8
C
I
R
C
U
L
A
R
-
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
3
1
9
+
=
31
3+1
4
=
=
4
=
4
-
-
3
-
18
3
21
12
1
18
+
=
76
7+6
13
1+3
=
4
=
4
-
8
C
I
R
C
U
L
A
R
-
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
12
1
18
+
=
85
8+5
13
1+3
=
4
=
4
-
-
3
9
9
3
3
3
1
9
+
=
40
4+0
4
-
=
4
=
4
-
8
C
I
R
C
U
L
A
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
3
3
3
-
-
-
-
3
occurs
x
4
=
12
1+2
3
4
-
-
-
-
-
-
-
1
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
-
-
9
-
-
9
occurs
x
3
=
27
2+7
9
32
8
C
I
R
C
U
L
A
R
-
-
13
-
-
8
-
40
-
13
3+2
-
3
-
-
3
3
3
-
-
-
-
3+0
-
-
-
-
4+0
-
3+0
5
8
C
I
R
C
U
L
A
R
-
-
3
-
-
8
-
4
-
3
-
-
3
9
9
3
3
3
6
9
-
-
-
-
-
-
-
-
-
-
5
8
C
I
R
C
U
L
A
R
-
-
3
-
-
8
-
4
-
3

 

 

-
8
C
I
R
C
U
L
A
R
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
+
=
9
=
9
-
=
8
=
8
-
-
-
9
-
-
-
-
-
-
+
=
9
=
9
-
=
8
=
8
-
8
C
I
R
C
U
L
A
R
-
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
3
1
9
+
=
31
3+1
4
=
=
4
=
4
-
-
3
-
18
3
21
12
1
18
+
=
76
7+6
13
1+3
=
4
=
4
-
8
C
I
R
C
U
L
A
R
-
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
12
1
18
+
=
85
8+5
13
1+3
=
4
=
4
-
-
3
9
9
3
3
3
1
9
+
=
40
4+0
4
-
=
4
=
4
-
8
C
I
R
C
U
L
A
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
-
3
-
-
3
3
3
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
9
9
-
-
-
-
9
-
-
9
occurs
x
3
=
27
2+7
9
32
8
C
I
R
C
U
L
A
R
-
-
13
-
-
8
-
40
-
13
3+2
-
3
-
-
3
3
3
-
-
-
-
3+0
-
-
-
-
4+0
-
3+0
5
8
C
I
R
C
U
L
A
R
-
-
3
-
-
8
-
4
-
3
-
-
3
9
9
3
3
3
6
9
-
-
-
-
-
-
-
-
-
-
5
8
C
I
R
C
U
L
A
R
-
-
3
-
-
8
-
4
-
3

 

 

-
14
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
6
-
9
6
5
+
=
35
3+5
8
-
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
15
-
9
15
14
+
=
62
6+2
8
-
=
8
=
8
-
14
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
3
1
9
-
4
-
2
-
-
-
+
=
37
3+7
10
1+0
=
1
=
1
-
-
3
-
18
3
21
12
1
18
-
13
-
20
-
-
-
+
=
109
1+0+9
10
1+0
=
1
=
1
-
14
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
12
1
18
-
13
15
20
9
15
14
+
=
171
1+7+1
9
-
=
9
=
9
-
-
3
9
9
3
3
3
1
9
-
4
6
2
9
6
5
+
=
72
7+2
9
-
=
9
=
9
-
14
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
3
3
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
-
1
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
15
14
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
30
-
-
14
-
72
-
27
1+5
1+4
-
9
9
-
-
-
-
9
-
-
-
-
9
-
-
-
-
3+0
-
-
1+4
-
7+2
-
2+7
6
5
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
3
-
-
5
-
9
-
9
-
-
3
9
9
3
3
3
6
9
-
4
6
6
9
6
5
-
-
-
-
-
-
-
-
-
-
6
5
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
3
-
-
5
-
9
-
9

 

 

14
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
6
-
9
6
5
+
=
35
3+5
8
-
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
15
-
9
15
14
+
=
62
6+2
8
-
=
8
=
8
14
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
3
1
9
-
4
-
2
-
-
-
+
=
37
3+7
10
1+0
=
1
=
1
-
3
-
18
3
21
12
1
18
-
13
-
20
-
-
-
+
=
109
1+0+9
10
1+0
=
1
=
1
14
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
12
1
18
-
13
15
20
9
15
14
+
=
171
1+7+1
9
-
=
9
=
9
-
3
9
9
3
3
3
1
9
-
4
6
2
9
6
5
+
=
72
7+2
9
-
=
9
=
9
14
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
3
3
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
1
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
9
9
-
-
-
-
9
-
-
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
14
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
30
-
-
14
-
72
-
27
1+4
-
9
9
-
-
-
-
9
-
-
-
-
9
-
-
-
-
3+0
-
-
1+4
-
7+2
-
2+7
5
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
3
-
-
5
-
9
-
9
-
3
9
9
3
3
3
6
9
-
4
6
6
9
6
5
-
-
-
-
-
-
-
-
-
-
5
C
I
R
C
U
L
A
R
-
M
O
T
I
O
N
-
-
3
-
-
5
-
9
-
9

 

 

4
C
I
R
C
U
L
A
R
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
6
-
9
6
5
+
=
35
3+5
8
-
=
8
=
8
-
-
9
-
-
-
-
-
-
-
15
-
9
15
14
+
=
62
6+2
8
-
=
8
=
8
14
C
I
R
C
U
L
A
R
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
3
1
9
4
-
2
-
-
-
+
=
37
3+7
10
1+0
=
1
=
1
-
3
-
18
3
21
12
1
18
13
-
20
-
-
-
+
=
109
1+0+9
10
1+0
=
1
=
1
14
C
I
R
C
U
L
A
R
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
12
1
18
13
15
20
9
15
14
+
=
171
1+7+1
9
-
=
9
=
9
-
3
9
9
3
3
3
1
9
4
6
2
9
6
5
+
=
72
7+2
9
-
=
9
=
9
14
C
I
R
C
U
L
A
R
M
O
T
I
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
3
3
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
1
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
9
9
-
-
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
4
=
36
3+6
9
14
C
I
R
C
U
L
A
R
M
O
T
I
O
N
-
-
30
-
-
14
-
72
-
27
1+4
-
9
9
-
-
-
-
9
-
-
-
9
-
-
-
-
3+0
-
-
1+4
-
7+2
-
2+7
5
C
I
R
C
U
L
A
R
M
O
T
I
O
N
-
-
3
-
-
5
-
9
-
9
-
3
9
9
3
3
3
6
9
4
6
6
9
6
5
-
-
-
-
-
-
-
-
-
-
5
C
I
R
C
U
L
A
R
M
O
T
I
O
N
-
-
3
-
-
5
-
9
-
9

 

 

-
19
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
-
-
8
-
-
-
-
-
-
-
-
6
-
-
-
8
-
-
-
9
-
-
-
-
+
=
31
3+1
=
4
-
4
=
4
-
-
-
8
-
-
-
-
-
-
-
-
15
-
-
-
8
-
-
-
9
-
-
-
-
+
=
40
4+0
=
4
=
4
=
4
-
19
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
-
2
-
5
-
3
7
3
3
5
-
-
6
-
2
-
5
-
3
-
9
3
3
5
+
=
64
6+4
=
10
1+0
1
=
1
-
-
20
-
5
-
3
25
3
12
5
-
-
6
-
20
-
5
-
3
-
18
3
12
5
+
=
145
1+4+5
=
10
1+0
1
=
1
-
19
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
-
20
8
5
-
3
25
3
12
5
-
15
6
-
20
8
5
-
3
9
18
3
12
5
+
=
185
1+8+5
=
14
=
5
=
5
-
-
2
8
5
-
3
7
3
3
5
-
6
6
-
2
8
5
-
3
9
9
3
3
5
+
=
95
9+5
=
14
1+4
5
=
5
-
19
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
-
-
-
--
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
-
3
3
-
-
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
6
=
18
1+8
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
3
=
18
1+8
9
5
19
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
40
-
-
19
-
95
-
41
-
1+9
-
-
-
-
3
-
3
3
-
-
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
4+0
-
-
1+9
-
9+5
-
4+1
5
10
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
4
-
-
10
-
14
-
5
-
1+1
2
8
5
-
3
7
3
3
5
-
6
6
-
2
8
5
-
3
9
9
3
3
5
-
-
-
-
-
1+1
-
1+4
-
-
5
1
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
4
-
-
1
-
5
-
5

 

 

19
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
-
8
-
-
-
-
-
-
-
-
6
-
-
-
8
-
-
-
9
-
-
-
-
+
=
31
3+1
=
4
-
4
=
4
-
-
8
-
-
-
-
-
-
-
-
15
-
-
-
8
-
-
-
9
-
-
-
-
+
=
40
4+0
=
4
=
4
=
4
19
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
2
-
5
-
3
7
3
3
5
-
-
6
-
2
-
5
-
3
-
9
3
3
5
+
=
64
6+4
=
10
1+0
1
=
1
-
20
-
5
-
3
25
3
12
5
-
-
6
-
20
-
5
-
3
-
18
3
12
5
+
=
145
1+4+5
=
10
1+0
1
=
1
19
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
20
8
5
-
3
25
3
12
5
-
15
6
-
20
8
5
-
3
9
18
3
12
5
+
=
185
1+8+5
=
14
=
5
=
5
-
2
8
5
-
3
7
3
3
5
-
6
6
-
2
8
5
-
3
9
9
3
3
5
+
=
95
9+5
=
14
1+4
5
=
5
19
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
3
-
3
3
-
-
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
6
=
18
1+8
9
-
-
-
5
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
3
=
18
1+8
9
19
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
40
-
-
19
-
95
-
41
1+9
-
-
-
-
3
-
3
3
-
-
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
4+0
-
-
1+9
-
9+5
-
4+1
10
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
4
-
-
10
-
14
-
5
1+1
2
8
5
-
3
7
3
3
5
-
6
6
-
2
8
5
-
3
9
9
3
3
5
-
-
-
-
-
1+1
-
1+4
-
-
1
T
H
E
-
C
Y
C
L
E
-
O
F
-
T
H
E
-
C
I
R
C
L
E
-
-
4
-
-
1
-
5
-
5

 

 

19
T
H
E
C
Y
C
L
E
O
F
T
H
E
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
-
8
-
-
-
-
-
-
6
-
-
8
-
-
9
-
-
-
-
+
=
31
3+1
=
4
-
4
=
4
-
-
8
-
-
-
-
-
-
15
-
-
8
-
-
9
-
-
-
-
+
=
40
4+0
=
4
=
4
=
4
19
T
H
E
C
Y
C
L
E
O
F
T
H
E
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
2
-
5
3
7
3
3
5
-
6
2
-
5
3
-
9
3
3
5
+
=
64
6+4
=
10
1+0
1
=
1
-
20
-
5
3
25
3
12
5
-
6
20
-
5
3
-
18
3
12
5
+
=
145
1+4+5
=
10
1+0
1
=
1
19
T
H
E
C
Y
C
L
E
O
F
T
H
E
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
20
8
5
3
25
3
12
5
15
6
20
8
5
3
9
18
3
12
5
+
=
185
1+8+5
=
14
=
5
=
5
-
2
8
5
3
7
3
3
5
6
6
2
8
5
3
9
9
3
3
5
+
=
95
9+5
=
14
1+4
5
=
5
19
T
H
E
C
Y
C
L
E
O
F
T
H
E
C
I
R
C
L
E
-
-
-
-
-
-
-
--
-
-
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
3
-
3
3
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
6
=
18
1+8
9
-
-
-
5
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
3
=
18
1+8
9
19
T
H
E
C
Y
C
L
E
O
F
T
H
E
C
I
R
C
L
E
-
-
40
-
-
19
-
95
-
41
1+9
-
-
-
3
-
3
3
-
-
-
-
-
-
3
-
-
3
3
-
-
-
4+0
-
-
1+9
-
9+5
-
4+1
10
T
H
E
C
Y
C
L
E
O
F
T
H
E
C
I
R
C
L
E
-
-
4
-
-
10
-
14
-
5
1+1
2
8
5
3
7
3
3
5
6
6
2
8
5
3
9
9
3
3
5
-
-
-
-
-
1+1
-
1+4
-
-
1
T
H
E
C
Y
C
L
E
O
F
T
H
E
C
I
R
C
L
E
-
-
4
-
-
1
-
5
-
5

 

 

3
THE
33
15
6
13
CIRCUMFERENCE
123
69
6
2
OF
21
12
3
1
A
1
1
1
6
CIRCLE
50
32
5
25
First Total
228
129
21
2+5
Add to Reduce
2+2+8
1+2+9
2+1
7
Second Total
12
12
3
-
Reduce to Deduce
1+2
1+2
-
7
Essence of Number
12
3
3

 

 

13
CIRCUMFERENCE
-
-
-
-
C
3
3
3
-
I
9
9
9
-
R
18
9
9
-
C
3
3
3
-
U
21
3
3
-
M+F+E
24
15
6
-
R
18
9
9
-
E+N+C+E
18
9
9
13
CIRCUMFERENCE
123
69
51
1+3
-
1+2+3
6+9
5+1
4
CIRCUMFERENCE
6
15
6
-
-
-
1+5
-
4
CIRCUMFERENCE
6
6
6

 

 

-
13
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
5
-
-
+
=
14
1+4
5
-
=
5
=
5
-
-
-
9
-
-
-
-
-
-
-
-
14
-
-
+
=
23
2+3
5
-
=
5
=
5
-
13
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
4
6
5
9
5
-
3
5
+
=
55
5+5
10
1+0
=
1
=
1
-
-
3
-
18
3
21
13
6
5
18
5
-
3
5
+
=
100
1+0+0
1
-
=
1
=
1
-
13
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
13
6
5
18
5
14
3
5
+
=
123
1+2+3
6
-
=
6
=
6
-
-
3
9
9
3
3
4
6
5
9
5
5
3
5
+
=
69
6+9
15
1+5
=
6
=
6
-
13
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
-
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
5
-
5
5
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
18
13
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
27
-
-
13
-
69
-
24
1+8
1+3
-
9
9
-
-
-
-
-
9
-
-
-
-
-
-
2+7
-
-
1+3
-
6+9
-
2+4
9
4
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
9
-
-
4
-
15
-
6
-
-
3
9
9
3
3
4
6
5
9
5
5
3
5
-
-
-
-
-
-
1+5
-
-
9
4
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
9
-
-
4
-
6
-
6

 

 

13
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
5
-
-
+
=
14
1+4
5
-
=
5
=
5
-
-
9
-
-
-
-
-
-
-
-
14
-
-
+
=
23
2+3
5
-
=
5
=
5
13
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
4
6
5
9
5
-
3
5
+
=
55
5+5
10
1+0
=
1
=
1
-
3
-
18
3
21
13
6
5
18
5
-
3
5
+
=
100
1+0+0
1
-
=
1
=
1
13
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
13
6
5
18
5
14
3
5
+
=
123
1+2+3
6
-
=
6
=
6
-
3
9
9
3
3
4
6
5
9
5
5
3
5
+
=
69
6+9
15
1+5
=
6
=
6
13
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
-
-
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
5
5
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
9
9
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
13
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
27
-
-
13
-
69
-
24
1+3
-
9
9
-
-
-
-
-
9
-
-
-
-
-
-
2+7
-
-
1+3
-
6+9
-
2+4
4
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
9
-
-
4
-
15
-
6
-
3
9
9
3
3
4
6
5
9
5
5
3
5
-
-
-
-
-
-
1+5
-
-
4
C
I
R
C
U
M
F
E
R
E
N
C
E
-
-
9
-
-
4
-
6
-
6

 

 

13
CIRCUMFERENCE
123
69
6
2
OF
21
12
3
1
A
1
1
1
6
CIRCLE
50
32
5
22
First Total
195
114
15
2+2
Add to Reduce
1+9+5
1+1+4
1+5
4
Second Total
15
6
6
-
Reduce to Deduce
1+5
-
-
4
Essence of Number
6
6
6

 

 

-
22
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
5
-
-
-
6
-
-
-
-
-
9
-
-
-
-
+
=
29
2+9
11
1+1
=
2
=
2
-
-
-
9
-
-
-
-
-
-
-
-
14
-
-
-
15
-
-
-
-
-
9
-
-
-
-
+
=
47
4+7
11
1+1
=
2
=
2
-
22
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
4
6
5
9
5
-
3
5
-
-
6
-
1
-
3
-
9
3
3
5
+
=
85
8+5
13
1+3
=
4
=
4
-
-
3
-
18
3
21
13
6
5
18
5
-
3
5
-
-
6
-
1
-
3
-
18
3
12
5
+
=
148
1+4+8
13
1+3
=
4
=
4
-
22
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
13
6
5
18
5
14
3
5
-
15
6
-
1
-
3
9
18
3
12
5
+
=
195
1+9+5
15
1+5
=
6
=
6
-
-
3
9
9
3
3
4
6
5
9
5
5
3
5
-
6
6
-
1
-
3
9
9
3
3
5
+
=
114
1+1+4
6
-
=
6
=
6
-
22
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
7
=
21
2+1
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
5
=
45
4+5
9
17
22
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
28
-
-
22
-
114
-
33
1+7
2+2
-
9
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
2+8
-
-
2+2
-
1+1+4
-
3+3
8
4
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
10
-
-
4
-
6
-
6
-
-
3
9
9
3
3
4
6
5
9
5
5
3
5
-
6
6
-
6
-
3
9
9
3
3
5
-
-
1+0
-
-
-
-
-
-
8
4
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
1
-
-
4
-
6
-
6

 

 

22
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
5
-
-
-
6
-
-
-
-
-
9
-
-
-
-
+
=
29
2+9
11
1+1
=
2
=
2
-
-
9
-
-
-
-
-
-
-
-
14
-
-
-
15
-
-
-
-
-
9
-
-
-
-
+
=
47
4+7
11
1+1
=
2
=
2
22
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
3
-
9
3
3
4
6
5
9
5
-
3
5
-
-
6
-
1
-
3
-
9
3
3
5
+
=
85
8+5
13
1+3
=
4
=
4
-
3
-
18
3
21
13
6
5
18
5
-
3
5
-
-
6
-
1
-
3
-
18
3
12
5
+
=
148
1+4+8
13
1+3
=
4
=
4
22
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
3
9
18
3
21
13
6
5
18
5
14
3
5
-
15
6
-
1
-
3
9
18
3
12
5
+
=
195
1+9+5
15
1+5
=
6
=
6
-
3
9
9
3
3
4
6
5
9
5
5
3
5
-
6
6
-
1
-
3
9
9
3
3
5
+
=
114
1+1+4
6
-
=
6
=
6
22
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
3
-
-
3
3
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
7
=
21
2+1
3
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
-
-
-
-
-
5
-
5
5
-
5
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
5
=
25
2+5
7
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
9
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
5
=
45
4+5
9
22
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
28
-
-
22
-
114
-
33
2+2
-
9
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
2+8
-
-
2+2
-
1+1+4
-
3+3
4
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
10
-
-
4
-
6
-
6
-
3
9
9
3
3
4
6
5
9
5
5
3
5
-
6
6
-
6
-
3
9
9
3
3
5
-
-
1+0
-
-
-
-
-
-
4
C
I
R
C
U
M
F
E
R
E
N
C
E
-
O
F
-
A
-
C
I
R
C
L
E
-
-
1
-
-
4
-
6
-
6

 

 

3
THE
33
15
6
4
LAMB
28
10
1
2
OF
21
12
3
3
GOD
26
17
8
12
Add to Reduce
108
54
18
1+2
Reduce to Deduce
1+0+8
5+4
1+8
3
Essence of Number
9
9
9

 

 

-
12
T
H
E
-
L
A
M
B
-
O
F
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
6
-
-
-
6
-
+
=
20
2+0
=
2
-
2
=
2
-
-
-
8
-
-
-
-
-
-
-
15
-
-
-
15
-
+
=
38
3+8
=
11
1+1
2
=
2
-
12
T
H
E
-
L
A
M
B
-
O
F
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
3
1
4
2
-
-
6
-
7
-
4
+
=
34
3+4
=
7
=
7
=
7
-
-
20
-
5
-
12
1
13
2
-
-
6
-
7
-
4
+
=
61
6+1
=
7
=
7
=
7
-
12
T
H
E
-
L
A
M
B
-
O
F
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
12
1
13
2
-
15
6
-
7
15
4
+
=
108
1+0+8
=
9
=
9
=
9
-
-
2
8
5
-
3
1
4
2
-
6
6
-
7
6
4
+
=
54
5+4
=
9
=
9
=
9
-
12
T
H
E
-
L
A
M
B
-
O
F
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
``-
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
NINE
-
-
-
-
-
-
9
12
T
H
E
-
L
A
M
B
-
O
F
-
G
O
D
-
-
36
-
-
12
-
54
-
45
-
1+2
-
-
-
-
-
-
-
-
-
6
6
-
-
6
-
-
-
3+6
-
-
1+2
-
5+4
-
4+5
9
3
T
H
E
-
L
A
M
B
-
O
F
-
G
O
D
-
-
9
-
-
3
-
9
-
9
-
1+2
2
8
5
-
3
1
4
2
-
6
6
-
7
6
4
-
-
-
-
-
-
-
-
-
-
9
3
T
H
E
-
L
A
M
B
-
O
F
-
G
O
D
-
-
9
-
-
3
-
9
-
9

 

 

P
=
7
-
5
PRIDE
52
34
7
G
=
7
-
8
GLUTTONY
134
35
8
G
=
7
-
5
GREED
39
30
3
W
=
5
-
5
WRATH
70
25
7
E
=
5
-
4
ENVY
66
21
3
L
=
3
-
4
LUST
72
18
9
S
=
1
-
5
SLOTH
74
20
2
W
-
35
4
36
First Total
507
183
39
-
-
3+5
-
3+6
Add to Reduce
5+0+7
1+8+3
3+9
-
-
8
-
9
Second Total
12
12
12
-
-
-
-
-
Reduce to Deduce
1+2
1+2
1+2
-
-
8
-
9
Essence of Number
3
3
3

 

 

8
EPIPHANY
94
49
4

 

 

4
FREE
34
25
7
6
GRATIS
74
29
2
10
Add to Reduce
108
54
9
1+0
Reduce to Deduce
1+0+8
5+4
-
1
Essence of Number
9
9
9

 

 

T
=
2
-
4
THOU
64
19
1
H
=
8
-
4
HAST
48
12
3
B
=
2
-
4
BEEN
26
17
8
W
=
5
-
7
WEIGHED
61
43
7
I
=
9
-
2
IN
23
14
5
T
=
2
-
3
THE
33
15
6
B
=
2
-
7
BALANCE
38
20
2
A
=
1
-
3
AND
19
10
1
F
=
6
-
5
FOUND
60
24
6
W
=
5
-
7
WANTING
88
34
7
W
-
42
4
46
First Total
460
208
46
-
-
4+2
-
4+6
Add to Reduce
4+6+0
2+0+8
4+6
-
-
6
-
10
Second Total
10
10
10
-
-
-
-
1+0
Reduce to Deduce
1+0
1+0
1+0
-
-
6
-
1
Essence of Number
1
1
1

 

 

T
=
2
-
4
THOU
64
19
1
H
=
8
-
4
HAST
48
12
3
W
-
10
4
8
Add to Reduce
112
31
4
-
-
1+0
-
-
Reduce to Deduce
1+1+2
3+1
-
-
-
1
-
8
Essence of Number
4
4
4

 

 

D
=
4
-
4
DULCE
45
18
9
E
=
5
-
2
`ET
25
7
7
D
=
4
-
7
DECORUM
79
34
7
E
=
5
-
3
EST
44
8
8
W
-
18
4
16
First Total
193
67
31
-
-
1+8
-
1+6
Add to Reduce
1+9+3
6+7
3+1
-
-
9
-
7
Second Total
13
13
4
-
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
9
-
7
Essence of Number
4
4
4

 

 

D
=
4
-
5
DEATH
38
20
2
R
=
9
-
5
RIDES
55
28
1
A
=
1
-
1
A
1
1
1
P
=
7
-
4
PALE
34
16
7
H
=
8
-
5
HORSE
65
29
2
W
-
29
4
20
First Total
193
94
13
-
-
2+9
-
2+0
Add to Reduce
1+9+3
9+4
1+3
-
-
11
-
2
Second Total
13
13
4
-
-
1+1
-
-
Reduce to Deduce
1+3
1+3
-
-
-
2
-
2
Essence of Number
4
4
4

 

 

9
GARIBALDI
63
45
9
8
GIUSEPPE
98
44
8
17
First Total
161
89
17
1+7
Add to Reduce
1+6+1
8+9
1+7
8
Second Total
8
17
8
-
Reduce to Deduce
-
1+7
-
8
Essence of Number
8
8
8

 

 

I

ME

GODS BUD GODS

ASTRAL

PROJECTIONS

ABOVE

AND

BEYOND

 

 

OF TIME AND STARS

Arthur C. Clarke 1972

The Sentinel

"I can never look now at the Milky Way without wondering from which of those banked clouds of stars the emissaries are coming. If you will pardon so commonplace a simile, we have set off the fire alarm and have nothing to do but wait.

I do not think we will have to wait for long."

 

 

GOD ONE GOD

AND ONE CHOSEN RACE THE HUMAN RACE

 

 

HOLY BIBLE

Scofield References

C 1 V 16

THE ACTS OF THE APOSTLES

Page 1148 (Part quoted)

"MEN AND BRETHREN THIS SCRIPTURE MUST NEEDS HAVE BEEN FULFILLED

WHICH THE HOLY GHOST BY THE MOUTH OF DAVID SPAKE"

 

 

THE

PROPHET

Kahil Gibran

Page 82/83/84/85/86

"If these be vague words, then seek not to clear them.

Vague and nebulous is the beginning of all things, but not their end,

And I would have you remember me as a beginning.

Life, and all that lives, is conceived in the mist and not in the crystal.

And who knows but a crystal is mist in decay

This would I have you remember in remembering me:

That which seems most feeble and bewildered in you is the strongest and most determined.

Is it not your breath that has erected and hardened the structure of your bones?

And is it not a dream which none of you remember having dreamt, that builded your city and fashioned all there is in it?

Could you but see the tides of that breath you would cease to see all else,

And if you could hear the whispering of the dream you would hear no other sound.

But you do not see, nor do you here, and it is well.

The veil that clouds your eyes shall be lifted by the hands that wove it,

And the clay that fills your ears shall be pierced by those fingers that kneaded it.

And you shall see

And you shall hear.

Yet you shall not deplore having known blindness, nor regret having been deaf

For in that day you shall know the hidden purposes in all things,

And you shall bless darkness as you would bless light.

After saying these things he looked about him,

and he saw the pilot of his ship standing by the helm

and gazing now at the full sails and now at the distance.

And he said:

Patient, over patient, is the captain of my ship.

The wind blows, and restless are the sails;

Even the rudder begs direction;

Yet quietly my captain awaits my silence.

And these my mariners, who have heard the

choir of the greater sea, they too have heard me

patiently.

Now they shall wait no longer.

I am ready

The stream has reached the sea, and once more

THE GREAT MOTHER

holds her son against her breast.

Fare you well, people of Orphalese.

This day has ended.

It is closing upon us even as the water-lily upon its own tomorrow.

What was given us here we shall keep,

And if it suffices not, then again must we come together and together

stretch our hands unto the giver.

Forget not that I shall come back to you.

A little while, and my longing shall gather dust and foam for another body.

A little while, a moment of rest upon the wind, and another woman shall bear me.

Farewell to you and the youth I have spent with you.

It was but yesterday we met in a dream.

You have sung to me in my aloneness, and I of your longings have built a tower in the sky.

But now our sleep has fled and our dream is over, and it is no longer dawn.

The noontide is upon us and our half waking has turned to fuller day, and we must part.

If in the twilight of memory we should meet once more,

we shall speak again together and you shall sing to me a deeper song.

and if our hands should meet in another dream we shall build another tower in the sky.

So saying he made a signal to the seamen,

and straightaway they weighed anchor and cast the ship loose from its moorings, and they moved eastward.

And a cry came from the people as from a single heart,

and it rose into the dusk and was carried out over the sea like a great trumpeting.

Only Almitra was silent, gazing after the ship until it had vanished into the mist.

And when all the people were dispersed she still stood alone upon the sea-wall,

remembering in her heart his saying:

A little while, a moment of rest upon the wind, and another woman shall bear me.'

 

A
=
1
-
1
A
1
1
1
L
=
3
-
6
LITTLE
78
24
6
W
=
5
-
5
WHILE
57
30
3
A
=
1
-
1
A
1
1
1
M
=
4
-
6
MOMENT
80
26
8
O
=
6
-
2
OF
21
12
3
R
=
9
-
4
REST
62
17
8
U
=
3
-
4
UPON
66
21
3
T
=
T
-
3
THE
33
15
6
W
=
W
-
4
WIND
50
23
5
A
=
1
-
3
AND
19
10
1
A
=
1
-
7
ANOTHER
81
36
9
W
=
5
-
5
WOMAN
66
21
3
S
=
1
-
5
SHALL
52
16
7
B
=
2
-
4
BEAR
26
17
8
M
=
4
-
2
ME
18
9
9
-
-
53
-
62
First Total
711
279
81
-
-
5+3
-
6+2
Add to Reduce
7+1+1
2+7+9
8+1
-
-
8
-
8
Second Total
9
18
9
-
-
-
-
-
Reduce to Deduce
-
1+8
-
-
-
8
-
8
Essence of Number
9
9
9

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1875-1955

Page 466

"Had not the normal, since time was, lived on the achievements of the abnormal? Men consciously and voluntarily descended into disease and madness, in search of knowledge which, acquired by fanaticism, would lead back to health; after the possession and use of it had ceased to be conditioned by that heroic and abnormal act of sacrifice. That was the true death on the cross, the true Atonement.

 

 

WAY OF THE PEACEFUL WARRIOR

A

BOOK THAT CHANGES LIVES

Dan Millman 1980

Page 44

"...do you recall that I told you we must work on changing your mind before you can see the warrior's way? / Page 45 /

"Yes, but I really don't think. . ."
"Don't be afraid," he repeated. "Comfort yourself with a say­ing of Confucius," he smiled. " 'Only the supremely wise and the ignorant do not alter.' " Saying that, he reached out and placed his hands gently but firmly on my temples.
Nothing happened for a moment-then suddenly, I felt a growing pressure in the middle of my head. There was a loud buzzing, then a sound like waves rushing up on the beach. I heard bells ringing, and my head felt as if it was going to burst. That's when I saw the light, and my mind exploded with its brightness. Something in me was dying-I knew this for a certainty-and something else was being born! Then the light engulfed everything."

 

 

THE WASTE LAND

and other poems 

T. S. Elliot 1940

Page 13

The Love Song of J. Alfred Prufrock

"I AM LAZARUS, COME FROM THE DEAD, COME BACK TO TELL YOU ALL I SHALL TELL YOU ALL"

 

 

THE LURE AND ROMANCE OF ALCHEMY.

A history of the secret link between magic and science

1990
C. J. S.Thompson

Page# 31 / 32

note 1 Julius Ruska ,Tabula Smaragdini 1926

"THE EMERALD TABLE OF HERMES: "

"True it is, without falsehood certain most true.That which is
above is like to that which is below, and that which is below is like
to that which is above, to accomplish the miracles of one thing.
And as in all things whereby contemplation of one, so in all things
arose from this one thing by a single act of adoption.
The father thereof is the Sun the mother the Moon.
The wind carried it in its womb,the earth is the source thereof.
It is the father of all works throughout the world.
The power thereof is perfect.
If it be cast on to earth, it will separate the element of earth
from that of fire, the subtle from the gross.
With great sagacity it doth ascend gently from earth to heaven.
Again it doth descend to earth and uniteth in itself from
things superior and things inferior.
Thus thou wilt possess the brightness of the world, and all
obscurity will fly far from thee.
This thing is the strong fortitude of all strength, for it over-
cometh every subtle thing and doth penetrate every solid substance.
Thus was this world created.
Hence will there be marvellous adaptations achieved of which
the manner is this.
For this reason I am called Hermes Trismegistus because I hold
three parts of the wisdom of the whole world.
That which I had to say about the operation of Sol is completed."

 

 

Freiheit - Keeping The Dream Alive lyrics. From the Original Motion Picture ... In my fantasy I remember their faces The hopes we had were much too high ... www.lyricsmode.com/lyrics/f/freiheit/keeping_the_dream_alive.html


Tonight the rain is falling
Full of memories of people and places
And while the past is calling
In my fantasy I remember their faces

The hopes we had were much too high
Way out of reach but we have to try
The game will never be over
Because we're keeping the dream alive

I hear myself recalling
Things you said to me
The night it all started
And still the rain is falling
Makes me feel the way
I felt when we parted

The hopes we had were much too high
Way out of reach but we have to try
No need to hide no need to run
'Cause all the answers come one by one
The game will never be over
Because we're keeping the dream alive

I need you
I love you

The game will never be over
Because we're keeping the dream alive

The hopes we had were much too high
Way out of reach but we have to try
No need to hide no need to run
'Cause all the answers come one by one

The hopes we had were much too high
Way out of reach but we have to try
No need to hide no need to run
'Cause all the answers come one by one

The game will never be over
Because we're keeping the dream alive

The game will never be over
Because we're keeping the dream alive

The game will never be over

Mmm mmm mmm mmm mmm mmm mmm mmm mmm.

 

 

I

SAY

IS THIS THE OTHER SIDE OF THE GREAT DIVIDE

?

NO ITS OVER THERE

I

HAVE JUST BEEN OVER THERE AND THEY SAID ITS OVER HERE

 

 

1
I
9
9
9
4
THAT
49
13
4
2
AM
14
5
5
11
TERRESTRIAL
145
55
1
16
EXTRATERRESTRIAL
213
78
6
3
AND
19
10
1
9
CELESTIAL
86
32
5
2
AM
14
5
5
1
I
9
9
9
49
First Total
558
216
45
4+9
Add to Reduce
5+5+8
2+1+6
4+5
13
Second Total
18
9
9
1+3
Reduce to Deduce
1+8
-
-
4
Essence of Number
9
9
9

 

 

Did Spacemen Colonise the Earth?

Robin Collyns 1974

Page 206

"FINIS"

 

 

THE MAGIC MOUNTAIN

Thomas Mann 1924

THE THUNDERBOLT

Page 715

"There is our friend, there is Hans Castorp! We recognize him at a distance, by the little beard he assumed 'while sitting at the " bad" Russian table. Like all the others, he is wet through and glowing. He is running, his feet heavy with mould, the bayonet swinging in his, hand. Look! He treads on the hand of a fallen comrade; with his hobnailed boot he treads the hand deep into the slimy, branch-strewn ground. But it is he. What, singing? As one sings, unaware, staring stark ahead, yes, thus. he spends his hurrying breath, to sing half soundlessly:

"And loving words I've carven
Upon its branches fair-"

He stumbles, No, he has flung himself down, a hell-hound is coming howling, a huge explosive shell, a disgusting sugar-loaf from the infernal regions. He lies with his face in the cool mire, legs. sprawled out, feet twisted, heels turned down. The product of a perverted science, laden with death, slopes earthward thirty paces in front of him and buries its nose in the ground; explodes inside there, with hideous expense of power, and raises up a fountain high as a house, of mud, fire, iron, molten metal, scattered fragments of humanity. Where it fell, two youths had lain, friends who in their need flung themselves down together - now they are scattered, commingled and gone.
Shame of our shadow-safety! Away! No more!-But our friend? Was he hit? He thought so, for the moment. A great clod of earth struck him on the shin, it hurt, but he smiles at it. Up he gets, and staggers on, limping on his earth-bound feet, all unconsciously singing:

"Its waving branches whiispered
A message in my ear -"

and thus, in the tumult, in the rain, in the dusk, vanishes out of our sight.
Farewell, honest Hans Castorp, farewell, Life's delicate child!
Your tale is told. We have told it to the end, and it was neither short nor long, but hermetic
. We have told it for its own sake, not for yours, for you were simple. But after all, it was your story, it befell you, you must have more in you than we thought; we will not disclaim the pedagogic weakness we conceived for / Page 716 / you in the telling; which could even lead us to press a finger delicately to our eyes at the thought that we shall see you no more, hear you no more for ever.
Farewell - and if thou livest or diest! Thy prospects are poor. The desperate dance, in which thy fortunes are caught up, will last yet many a sinful year; we should not care to set a high stake on thy life by the time it ends. We even confess that it is without great concern we leave the question open. Adventures of the flesh and in the spirit, while enhancing thy simplicity, granted thee to know in the spirit what in the flesh thou scarcely couldst have done. Moments there were, when out of death, and the rebellion of the flesh, there came to thee, as thou tookest stock of thyself, a dream of love. Out of this universal feast of death, out of this extremity of fever, kindling. the rain-washed evening sky to a fiery glow, may it be that Love one day shall mount?

FINIS OPERIS

 

 
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