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Rekna · 08-25-2004, 05:55 PM

Let's talk about the number Phi (1.61803399), which is also known as the golden ratio.

Phi is a very special number, a number that makes Pi look insignificant in comparison. Yet many people have never even heard of Phi.

I first learned about Phi as an undergraduate doing a BS in mathematics. First let's calculate Phi. Many of you have probably heard of the Fibonacci sequence, a sequence where you add the previous two numbers of the sequence to get the next number.

The Fibonacci sequence that is the most well known is the following:

1,1,2,3,5,8,13,21,34,ect,ect

Now Phi is calculated by taking any number in the sequence divided by the previous. The farther you are in the sequence the closer to phi you are. That is the ratio of the sequence converges to Phi.

This chart illustrates this:

N F(N) Ratio
0 1 1
1 1 2
2 2 1.5
3 3 1.666666667
4 5 1.6
5 8 1.625
6 13 1.615384615
7 21 1.619047619
8 34 1.617647059
9 55 1.618181818
10 89 1.617977528
11 144 1.618055556
12 233 1.618025751
13 377 1.618037135
14 610 1.618032787
15 987 1.618034448
16 1597 1.618033813
17 2584 1.618034056
18 4181 1.618033963
19 6765 1.618033999
20 10946 ------------

So big deal right? Well it gets interesting if we change the starting numbers the ratio will still converge to Phi.

N F(N) Ratio
0 5 0.6
1 3 2.666666667
2 8 1.375
3 11 1.727272727
4 19 1.578947368
5 30 1.633333333
6 49 1.612244898
7 79 1.620253165
8 128 1.6171875
9 207 1.618357488
10 335 1.617910448
11 542 1.618081181
12 877 1.618015964
13 1419 1.618040874
14 2296 1.618031359
15 3715 1.618034993
16 6011 1.618033605
17 9726 1.618034135
18 15737 1.618033933
19 25463 1.61803401
20 41200 ------------

N F(N) Ratio
0 1 43
1 43 1.023255814
2 44 1.977272727
3 87 1.505747126
4 131 1.664122137
5 218 1.600917431
6 349 1.624641834
7 567 1.615520282
8 916 1.618995633
9 1483 1.617666891
10 2399 1.618174239
11 3882 1.617980422
12 6281 1.61805445
13 10163 1.618026173
14 16444 1.618036974
15 26607 1.618032848
16 43051 1.618034424
17 69658 1.618033822
18 112709 1.618034052
19 182367 1.618033964
20 295076 ------------

This alone is an oddity. But since we are using a pattern it can be easily explained. The fact any Fibonacci sequence converges to this ratio is not what makes it so significant. First this number turns up in mathematics all the time. This ratio appears everywhere, especially in many geometric shapes. I don’t want to go into to many details on this because again it is unimportant that it shows up in math.

What is truly amazing about Phi is how often it shows up in nature! Phi appears EVERYWHERE in nature. Animals from all over exhibit this ratio in their body. The following website illustrates some of the places this number appears in nature: http://evolutionoftruth.com/div/nature.htm . This number shows up in butterflies, dolphins, ants, sea shells, and more importantly people. Phi shows up all over the human body for example: (from http://students.bath.ac.uk/ma1cam/GRnat.html) “If you take the length of the last digit on one of your fingers and multiply it by Phi you get the length of the digit before it, this can be repeated for the next digit, and the bones in the hand.” The same is true with your arms, legs, ect. In fact Leonardo Divinchi used phi in his paintings to make his people look more realistic. I’m not kidding this number appears everywhere in nature. And it isn’t all biological either; it appears in galaxies, hurricanes, ect.

Here are some more links on Phi.

http://courses.ncssm.edu/compton/geo...erm/divine.htm
http://www.space.com/scienceastronom...ls_030917.html
http://www.championtrees.org/yarrow/phi/phi.htm

Ok so now comes why I posted this in this forum. There is clearly something non-random happening throughout everything in the universe. This number pops up far to often to be random. Because of how often it comes up and how impossible it would just a random coincidence this number is sometimes called the divine ratio.

So my question is how can something occur so frequently and so perfectly and not be caused by something? To me this is the single greatest fact pointing to a higher being, some sort of creator of the universe. I’d love to see someone explain Phi without acknowledging the very likely existence of a divine creator.

In addition to phi there is also Pi and e which tend to pop up a lot.

08-25-2004, 05:55 PM	#1 (permalink)
Rekna Junkie	1.61803399 (Phi) Let's talk about the number Phi (1.61803399), which is also known as the golden ratio. Phi is a very special number, a number that makes Pi look insignificant in comparison. Yet many people have never even heard of Phi. I first learned about Phi as an undergraduate doing a BS in mathematics. First let's calculate Phi. Many of you have probably heard of the Fibonacci sequence, a sequence where you add the previous two numbers of the sequence to get the next number. The Fibonacci sequence that is the most well known is the following: 1,1,2,3,5,8,13,21,34,ect,ect Now Phi is calculated by taking any number in the sequence divided by the previous. The farther you are in the sequence the closer to phi you are. That is the ratio of the sequence converges to Phi. This chart illustrates this: N F(N) Ratio 0 1 1 1 1 2 2 2 1.5 3 3 1.666666667 4 5 1.6 5 8 1.625 6 13 1.615384615 7 21 1.619047619 8 34 1.617647059 9 55 1.618181818 10 89 1.617977528 11 144 1.618055556 12 233 1.618025751 13 377 1.618037135 14 610 1.618032787 15 987 1.618034448 16 1597 1.618033813 17 2584 1.618034056 18 4181 1.618033963 19 6765 1.618033999 20 10946 ------------ So big deal right? Well it gets interesting if we change the starting numbers the ratio will still converge to Phi. N F(N) Ratio 0 5 0.6 1 3 2.666666667 2 8 1.375 3 11 1.727272727 4 19 1.578947368 5 30 1.633333333 6 49 1.612244898 7 79 1.620253165 8 128 1.6171875 9 207 1.618357488 10 335 1.617910448 11 542 1.618081181 12 877 1.618015964 13 1419 1.618040874 14 2296 1.618031359 15 3715 1.618034993 16 6011 1.618033605 17 9726 1.618034135 18 15737 1.618033933 19 25463 1.61803401 20 41200 ------------ N F(N) Ratio 0 1 43 1 43 1.023255814 2 44 1.977272727 3 87 1.505747126 4 131 1.664122137 5 218 1.600917431 6 349 1.624641834 7 567 1.615520282 8 916 1.618995633 9 1483 1.617666891 10 2399 1.618174239 11 3882 1.617980422 12 6281 1.61805445 13 10163 1.618026173 14 16444 1.618036974 15 26607 1.618032848 16 43051 1.618034424 17 69658 1.618033822 18 112709 1.618034052 19 182367 1.618033964 20 295076 ------------ This alone is an oddity. But since we are using a pattern it can be easily explained. The fact any Fibonacci sequence converges to this ratio is not what makes it so significant. First this number turns up in mathematics all the time. This ratio appears everywhere, especially in many geometric shapes. I don’t want to go into to many details on this because again it is unimportant that it shows up in math. What is truly amazing about Phi is how often it shows up in nature! Phi appears EVERYWHERE in nature. Animals from all over exhibit this ratio in their body. The following website illustrates some of the places this number appears in nature: http://evolutionoftruth.com/div/nature.htm . This number shows up in butterflies, dolphins, ants, sea shells, and more importantly people. Phi shows up all over the human body for example: (from http://students.bath.ac.uk/ma1cam/GRnat.html) “If you take the length of the last digit on one of your fingers and multiply it by Phi you get the length of the digit before it, this can be repeated for the next digit, and the bones in the hand.” The same is true with your arms, legs, ect. In fact Leonardo Divinchi used phi in his paintings to make his people look more realistic. I’m not kidding this number appears everywhere in nature. And it isn’t all biological either; it appears in galaxies, hurricanes, ect. Here are some more links on Phi. http://courses.ncssm.edu/compton/geo...erm/divine.htm http://www.space.com/scienceastronom...ls_030917.html http://www.championtrees.org/yarrow/phi/phi.htm Ok so now comes why I posted this in this forum. There is clearly something non-random happening throughout everything in the universe. This number pops up far to often to be random. Because of how often it comes up and how impossible it would just a random coincidence this number is sometimes called the divine ratio. So my question is how can something occur so frequently and so perfectly and not be caused by something? To me this is the single greatest fact pointing to a higher being, some sort of creator of the universe. I’d love to see someone explain Phi without acknowledging the very likely existence of a divine creator. In addition to phi there is also Pi and e which tend to pop up a lot. Last edited by Rekna; 08-25-2004 at 06:12 PM..