Magical Phi & phi
This animation above represents the expansion of the continuing
fraction of the irrational number phi. Irrational hence the
difference, for example, between the ratio of two 5 placed numbers
and two 15 place numbers approaches zero.
The irrational number phi, also called the golden ratio is the
natural ratio most pleasing to the eye, used in art naturally. Here
it is derived from the ratio of successive numbers in the Fibonacci's Series arrived at by adding the previous
two numbers,.. here the first 100
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,
1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393,
196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887,
9227465, 14930352, 24157817, 39088169, 63245986, 102334155,
165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903,
2971215073, 4807526976, 7778742049, 12586269025, 20365011074,
32951280099, 53316291173, 86267571272, 139583862445, 225851433717,
365435296162, 591286729879, 956722026041, 1548008755920,
2504730781961, 4052739537881, 6557470319842, 10610209857723,
17167680177565, 27777890035288, 44945570212853, 72723460248141,
117669030460994, 190392490709135, 308061521170129, 498454011879264,
806515533049393, 1304969544928657, 2111485077978050,
3416454622906707, 5527939700884757, 8944394323791464,
14472334024676220, 23416728348467684, 37889062373143900,
61305790721611580, 99194853094755490, 160500643816367070,
259695496911122560, 420196140727489660, 679891637638612200,
1100087778366101900, 1779979416004714000, 2880067194370816000,
4660046610375530000, 7540113804746346000, 12200160415121877000,
19740274219868225000, 31940434634990100000, 51680708854858330000,
83621143489848420000, 135301852344706760000, 218922995834555200000,
354224848179262800000,
573147844013817200000,
Here the ratio:
