"While the Golden Section, phi, is the basis for the dynamic geometry of Nature, static geometry
is based on pi: 3.141592653589 etc. Pi exists primarily in the mind and mathematics of Humans.
The dynamic energy within Nature distorts a true circle or sphere." jeb
Phi and Pi can be calculated to millions of decimal places with no apparant pattern
however they are intrinsically related to one another.
.3 x 2.61803399 = .78541019
3.14159253 / 4 = .78539816
difference = .00001203
ratio: 1.00001531
One way of achieving a close approximation of pi
is through the square root of phibo #16, 987:
(987.5 / 10) = 3.141655614
pi = 3.141592653
diff = .000062961
ratio: 1.00002004
An approximation of phi from the 10th root of 123, (lucas #10)
123.1 = 1.618044685
phi = 1.618033988
diff = .000010697
ratio: 1.00000661
In the context of lix pi is usually represented by the letter "C" = 355/113. This ratio,
rediscovered in the 15th Century by Adriaan Anthonizoon is generated by pairing
the first three odd numbers: 1 1 3 3 5 5, then divide the last three digits
by the first three to achieve a fairly close approximation of pi.
355 / 113 = 3.14159292
pi = 3.14159265
diff = .00000027
ratio: 1.00000008
first 3 digits of pi total 8
first 3 digits of phi total 8
first 8 digits of pi total 31
the first 8 digits of phi total 31
13th and 15th digit of pi and phi is 9
314159 and 1618033 are prime numbers
Both pi and phi contain 6 "bookended" numbers:
pi: 141, 535, 979, 323 626, 383 in the first 28 digits
phi: 161, 989, 484, 868,343, 656 in the first 32 digits
pi, phi and 33
31415
+ 1618
33033
the first "0" in pi occurs at the 33 digit
there is also a 0 at digit 55 and 66
there are 33 digits between the first three 0's of phi.
the first 7 phibonacci numbers total 33
1 + 1 + 2 + 3 + 5 + 8 + 13 =
In the following table the first 42 digits of pi and phi are separated into groups of six.
The row beneath is the sum of the six above.
The third row is the sum of the first 18, 30 and 42 digits.
At 18 pi total is 85 and phi is 100.
At 42: pi = 201, phi = 200
| 314159 |
265358 |
979323 |
846264 |
338327 |
950288 |
419716 |
| 23 |
29 |
33 |
30 |
26 |
32 |
28 |
| 85 |
141 |
201 |
||||
| 161803 |
398874 |
989484 |
820458 |
683436 |
563811 |
772030 |
| 19 |
39 |
42 |
27 |
30 |
24 |
19 |
| 100 |
157 |
200 |
While it might seem insignificant the first 18 digits of phi total 100 and the first 42 total 200
consider that no other "hundreds" appear on an exact digit in the first 300 digits of either pi or phi
with the mind boggling exception of these two:
the digits of pi add to 1000 on #217, a 1
the digits of phi add to 1000 on #221, also a 1
pi 126 + = 588 = 12 x 49
phi 126 + = 582 = 6 x 97
dif: 6
pi 242 + = 1139 = 17 x 67
phi 242 + = 1133 = 11 x 103
dif : 6
the phibonacci series starts again every 300 additions.
the first 300 digits of pi total 1339 = 13 x 103
the first 300 digits of phi total 1369 = 372
dif: 30
" Pi is one of the most beautiful things in the world and if i can share that joy in numbers, if i can share that
in some small measure with the world, through my writing and through my speaking, then I feel that i've
done something useful." Daniel Tammet, in March 2004 recited 22,514 digits of pi from memory, without error.
back to the lix unit
©
stephen langton goulet