This conversation is closed.

## Phi or the golden ratio

For, about 2400 years, humans are fascinated with the number Phi which is calculated as (1+ square root of 5) divided by 2 giving us the result of 1.61803...

Not only is this ratio often used in art, architecture and design, but is also seems to be a common ratio in nature.

What do you think, is the occurrence of the golden ratio in nature just a coincidence or is there more to it ?

If so, what could explain that that this ratio is so common in nature ?

## Justin Dumas

## Harald Jezek 50+

## Pabitra Mukhopadhyay 50+

1. Ask why mountains are mostly cone shaped. 'Phi' may be common in nature as the spatial growth of complex biological systems finds this ratio as the simplest expansion route. It may be argued that other different proportions were blindly tried by nature and they just lost out in the evolutionary trial and error.

2. Another somewhat different but equally plausible cause is related to the fact that most often the claims of accuracy of the proportions in natural bodies to be exactly phi is inaccurate. Arts and architecture are different, they are intentionally created to match this ratio. But on account of a phenomenon called pareidolia our pattern seeking brains conjure up this ratio in nature.

Fritzie's comment is interesting, thanks to her.

## John Mauren

The following is a poem I wrote a while back that further illustrates my point:

Groups that Lie, Root their Systems in Vectors gone awry

Conflicts arise, as manifest patterns become the linear structures for life to survive.

Of salient transcription, notational in and of the principally framed

We seek to maintain grandiose, semiotic paradigm's begetting invariant claims

Dimensionally unified, the intangible are expressed by the formulations of mind

Fighting for stasis, a basis for attaining solidification of place in time.

The following video will most likely answer most Harald Jezek's questions:

The Golden Ratio & Fibonacci Numbers: Fact versus Fiction

(October 8, 2012) Professor Keith Devlin dives into the topics of the golden ratio and fibonacci numbers. Originally presented in the Stanford Continuing Studies Program.

http://www.youtube.com/watch?v=4oyyXC5IzEE

## Harald Jezek 50+

## Harald Jezek 50+

As to point 2: This is certainly true. Even in the case of the Fibonacci numbers the ratio between one and another one is not exactly Phi.

## Fritzie - 200+

The golden ratio is simply the ratio of the long side to the short side of the "brick." Many people believe these proportions are more visually appealing than longer skinnier rectangles or more square ones.

Another entry point in thinking about phi starts with the Fibonacci numbers, which many of the younger people here have probably seen. The sequence goes 1 1 2 3 5 8 13 21 34 and so forth. The rule for making this sequence is easy to see if you look at any three consecutive numbers in the series. Add the first two and you get the third. If you count the number of little sections in the rows of pineapples and pine cones, they pretty much follow a fibonnacci sequence. And as you keep generating more numbers in that sequence, you find that the ratio of a fibonacci number to the one before it gets closer and closer to phi as the numbers get larger.

## Harald Jezek 50+

## Fritzie - 200+

The reason I mentioned the Fibonacci sequence is that seeing that the rule for generating the next number on the list has such a simple sort of form makes it easier to believe such a pattern might be common in nature. Similarly, seeing a visual representation of the square, the triangular, and the hexagonal numbers makes it easier to see why those also might appear commonly in nature.

It only seems bizarre when you look at the numbers without the simple generating algorithm.

## Harald Jezek 50+

## Fritzie - 200+

## Harald Jezek 50+

## Fritzie - 200+

I would not remember either from Angels and Demons except that, as a former math teacher, I knew whenever I assigned students to write a short article on an interesting idea in mathematics (which I needed to approve to avoid redundancy), the first topic any student put forward was always phi, because they had all read much about it in Dan Brown.

## Harald Jezek 50+

Btw, are you German ? Just guessing from your name ;-)

## Fritzie - 200+

## Harald Jezek 50+

## Francois le Roux

Start with the videos in order preferably but in the first video it only starts mainly at 1:50

http://www.youtube.com/watch?v=ahXIMUkSXX0

http://www.youtube.com/watch?v=lOIP_Z_-0Hs&feature=youtu.be

http://www.youtube.com/watch?v=14-NdQwKz9w&feature=youtu.be

## Steve C

Perhaps it's just the sub-atoms making use of the various sub-atomic forces efficiently - you know - those crazy lines that come out of atom-smashers.

My only other guess is that is how we want to see the measurements come-out; as even measurements are guesses, (biased guesses in the end), if you look close-enough.

BTW, the best "Why" I've found so-far, by-far, is Stan Tenen's Meru Foundation work. (That is, "if you're tired of the rusty-old gold or platinum explanations.")

## Ang Perrier 10+

Nature has figured out the most effective way to grow things. There is some efficiency connected to this particular calculation that provides nature with the most efficient way to produce and grow.

## Nik Cronin

Makes sense if the universe is computing reality as it goes along.

Information using energy to produce complexity.

## Harald Jezek 50+

The deeper we dig into the secrets of the universe the less we are able to describe things in words and the more we need mathematics to describe reality.

## Nik Cronin

A crude analogy with a computer maybe, the energy is electrical, the "force" is human, the tools are logical programs and the output is to all intents and purposes magical, but the engine is pure number in ordered motion.

## Samuel Warren

Check it out if ya can,

http://www.ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers.html

## Fritzie - 200+

## Harald Jezek 50+