Just what is the "golden ratio number". Someone earlier said it proved the existence of God.?

Question

Not what I was finding. Thoughts?

Answer 1

The golden ratio is (1+√5)/2. It is supposed to be a pleasing proportion in art, and appears in nature. It doesn't prove anything.

Answer 2

Suppose you have a line segment with a total length a+b. The line is split into 2 parts with the 1st part of length a and the second part of length b. The golden ratio can be derived by finding a and b such that the ratio of the first to the second is the same as the ratio of the whole line to the first (or a+b is to a as a is to b)

Mathematically this is expressed as

(a+b)/a = a/b = φ
1 + b/a = φ
b/a = φ - 1

using a/b = φ

φ - 1 = 1/φ

φ² - φ - 1 = 0

solving the quadratic equation,

φ = ½([1±√5)

since the negative solution results in a negative ratio

φ = ½(1+√5)

If this were really a proof of god then I'd be mighty impressed with myself.

Answer 3

There are no proofs that god exists, nor any that god doesn't exist. God is simply a concept totally outside the realm of scientific thought (and should therefore, in my opinion, be ignored).

Let's say you had a rectangle with sides of a certain ratio. When you slice this rectangle in half, you end up with two more rectangles that each have the same ratio of sides. There's only one ratio of sides that satisfies this property, and it's the golden ratio.

Let's say you had a Fibonacci sequence, where you form the next term by adding the two previous terms:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...
As you keep going up this series, the ratio of the term to the term before it approaches the golden ratio.

Let's say you drew a precise pentagram like this one:
http://en.wikipedia.org/wiki/Image:Pentagram-phi.svg
In this picture, the ratio of the red segment to the green one is the golden ratio. The ratio of green to blue is the golden ratio. The ratio of blue to pink is the golden ratio as well.

The golden ratio, written in its simplest form is just
(1 + sqrt(5)) / 2
or
1.618033988749895... (a never-ending, non-repeating decimal)

Answer 4

If God liked nice shapes, this would provide evidence. The one I know is [1+sqrt(5)]/2