Can anyone tell me what makes the golden ratio so important?

Question

I know what the golden ratio stands for but why is this number special? How does it relate to the Fibonacci sequence? What is it's role in greek and egyptian architechture?

Answer 1

the golden ratio = 1.61803399

Here is a 'Fibonacci series'.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ..

If we take the ratio of two successive numbers in this series and divide each by the number before it, we will find the following series of numbers.

1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.6666...
8/5 = 1.6
13/8 = 1.625
21/13 = 1.61538...
34/21 = 1.61904...

The ratio seems to be settling down to a particular value, which we call the golden ratio(Phi=1.618..).



Golden Rectangle is a rectangle with proportions that are two consecutive numbers from the Fibonacci sequence.

The Golden Rectangle has been said to be one of the most visually satisfying of all
geometric forms. We can find many examples in art masterpieces such as in edifices of ancient Greece.


it's even important in Mona Lisa! InWe can draw a rectangle whose base extends from the woman's right wrist to her left elbow and extend the rectangle vertically until it reaches the very top of her head. Then we will have a golden rectangle.
Also, if we draw squares inside this Golden Rectangle, we will discover that the edges of these new squares come to all the important focal points of the woman: her chin, her eye, her nose, and the upturned corner of her mysterious mouth.
It is believed that Leonardo, as a mathematician tried to incorporate of mathematics into art. This painting seems to be made purposefully line up with golden rectangle.


i hope this has helped!

~MathWhiz~

Answer 2

Hahahah, I agree all he does is dunk from alley oops or putbacks. He will make a hook shot every once in a while but you can give him that because he is not consistent with it. No wonder Shaq always makes fun of him hahaha, but his defense is good and rebounding can change the game. D12 has good potential if he worked on his moves more than his biceps because he could do some serious damage offensively on bigger opponents like Shaq instead of Big Z. You have a good point with the assist he should be getting because he does get DT a lot. There is nothing here that I do not disagree about.

Answer 3

It's apeared in lots of random things. For the Fibonacci sequence (1,1,2,3,5,8,...a,b) as it continutes b/a aproaches phi. Much of greek and egyptian architechture has ratios that are close to phi, but are often just close to 1.6