Where in nature do we find the golden ratio?

Question

I know about some of them like the Nautilus shell, the head of a daisy or sunflower, pineapples, pinecones and some other seeds and fruit. Are there any animals that follow this ratio or the Fibbonacci sequence? How can we explain this ingenious method of nature scientifically? Natural selection?

Answer 1

you find when you see people running round in circles and disappearing up their own a*s-holes

Answer 2

Some specific proportions in the bodies of many animals (including humans) are often claimed to be in the golden ratio. There is actually a large variation in the real measures of these elements in a specific individual and the proportion in question is often significantly different from the golden ratio. Nevertheless, some of these ratios are observed to be quite close to the golden ratio in the shape of the organs or parts which closely follow some basic geometrical shape . The ratio of successive phalangeal bones of the digits and the metacarpal bone approximates the golden ratio.

I've also read of studies that indicate that people considered beautiful or handsome have facial features that conform to the golden ratio.

Answer 3

You can see it seashells like Nautilus and the Tibia Shell Spiral. Animals like a Trout, of Blue Angle Fish,
Architecture like the Notre Dame Cathedral in Paris.
The posters Folies-Bergere by Jules Cheret and Bauhaus Ausstellung by Friz Schleifer.
The Volkswagon Beetle.

Pick up the book "Geometry of Design" by Kimberly Elam, very very good source.

Answer 4

You can find it also in leaf arrangements, family trees (examples with rabbits, bees, cows..), and also have the golden ratio in some parts of our body:
"Lastly, it is interesting to note that the golden proportion is also clearly evident in the human figure: one's upper leg can often be found to be Phi times ones lower leg; ones eyes are usually about Phi of the way up from the chin. In the picture below we see that the proportion of adjacent teeth is also phi (a set gauge is being used to measure the teeth). Indeed, it has been argued that what we perceive as beauty in a person is determined largely by the closeness of their proportions (both in face and figure) to the golden mean. " http://students.bath.ac.uk/ma1caab/nature.html

Also the length of the finger bones have the Fibonacci ratio.

Answer 5

The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron. It is denoted , or sometimes . The designations "phi" (for ) and "Phi" (for the golden ratio conjugate ) are sometimes also used (Knott).

I.e
It simply means the patter of growth governed by the golden ratio, snails (chambers in their shells) flowers for petals etc.

Answer 6

R U talking about PHI. It's mentioned in the Da vInci Code. Very interesting topic

Answer 7

In humans:
1)your height from head to toe divided by the height from your navel to your toes.
2)the length of your shoulder to fingertips divided by length of your elbow to fingertips.
3)length of hand divided by length of finger

Answer 8

snails and some shell fish

Answer 9

Ammonites have it aswell.

Answer 10

I do not know