can u find some example of golden ratio in nature?

Answer 1

the golden ratio can be found in the limbs of the human body
Da Vinci suggested that the human body has proportions close to the golden ratio. The Swiss architect Le Corbusier took this suggestion to an extreme, not only splitting the body's height at the navel into two sections in the golden ratio, but splitting those each again, at the knees and at the throat.
Fibonacci numbers and the Golden Mean appear everywhere in nature. The pattern by which seeds are arranged on a seed head is the same as that by which leaves are arranged around a stem, or petals around a flower.

For example, new cells are created only at the very tip (meristem) of a growing plant. They are formed in a spiral, with Phi new cells being built in every revolution of the meristem. This process of growth carries through all aspects of a plant's structure: there will be Phi leaves in every full rotation around the stem, Phi seeds each time around the seed head, Phi branches growing per rotation of the tree trunk and so on. (Note: Phi seeds (for example) placed per turn is the same as saying phi turns per seed placed).

This is no mere coincidence - it is 'natures way' of optimizing structures. Rotating by phi guarantees equal spacing of leaves and seeds no matter how far from the central starting point you go. This picture, showing the centre of a cone flower, illustrates that fact: notice how by one set rule (rotation by phi) the seeds are placed such that they are neither overcrowded in the middle nor sparse around the edges.

Plants naturally grow in such a way as to ensure the maximum possible exposure to light on each leaf - arranging them at Phi per turn addresses the potential problem of the upper leaves overshadowing the lower ones, and also leaves the largest possible surface area open to catch rain water and direct it down the stem to the roots.

But why phi turns? Will not any angle produce results to the same effect? Strangely, most angles do not even come close to being suitable, and the extent to which they differ from phi is remarkable. Try to imagine o.5 turns per seed placed. Then we get two 'arms' of seeds projecting from the centre, and the rest of the area is completly empty.

Answer 2

FIBONACCI IN NATURE


The Fibonacci numbers play a significant role in nature and in art and architecture. We will first use the rectangle to lead us to some interesting applications in these areas.
We will construct a set of rectangles using the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, and 34 which will lead us to a design found in nature. You will need a ruler, protractor, and compass.
Start by drawing two, unit squares (0.5 cm is suggested) side by side. Next construct a 2-unit by 2-unit square on top of the two, unit squares. Next draw a square along the edge which borders both a unit square and the size 2 square (that is, a 3-unit square). The next square will border the 2-unit and the 3-unit squares, and each successive square will have an edge which is the sum of the two squares immediately preceding it. Continue until you have drawn a final square bordering the 13-unit and 21 unit squares.
Your construction will look like this:
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Now, with your compass, starting in the unit squares, construct in each square an arc of a circle with a radius the size of the edge of each respective square (Your arcs will be quarter circles.).
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This spiral construction closely approximates the spiral of a snail, nautilus, and other sea shells.

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We will next consider the use by architects and artists throughout history of the "Golden Ratio" and other geometric shapes based upon these ratios.
Graphics courtesy of Dr. Ron Knott, FIMA, C.Math, MBcs,C.Eng, Dept. of Mathematical and Computing Sciences, Univerity of Surrey, UK

Phi and the Egyptian Pyramids?
The Rhind Papyrus of about 1650 BC is one of the oldest mathematical works in existence, giving methods and problems used by the ancient Babylonians and Egyptians. It includes the solution to some problems about pyramids but it does not mention anything about the golden ratio Phi.
The ratio of the length of a face of the Great Pyramid (from centre of the bottom of a face to the apex of the pyramid) to the distance from the same point to the exact centre of the pyramid's base square is about 1·6. It is a matter of debate whether this was "intended" to be the golden section number or not.
According to Elmer Robinson (see the reference below), using the average of eight sets of data, says that "the theory that the perimeter of the pyramid divided by twice its vertical height is the value of pi" fits the data much better than the theory above about Phi.
The Fibonacci Drawing Board Design of the Great Pyramid of Gizeh Col. R S Beard in Fibonacci Quarterly vol 6, 1968, pages 85 - 87;
has three separate theories (only one of which involves the golden section) which agree quite well with the dimensions as measured in 1880.

Answer 3

In the world 80% poor people, and 20% rich people, but now the ratio turns to 90% poor people, and 10% rich people.

Answer 4

some branches and a pinapple. If you look at the pinapple it will follow the golden ratio.

Answer 5

pine cones, conch shells, pineapples, daisies, sunflowers

Answer 6

i find them everytime i watch Pi