Consider the line above. We'll start by drawing some line AC. Then we'll divide that line by placing the B such that the following is true:

AB is to BC as BC is to AC

We can write an equation to express this relationship as:

AB/BC = BC/AC.

Let's suppose AB is 1 unit. Could be 1 inch, 1 millimeter, 1 foot, whatever. Let's then define BC = x. Then AC = (1 + x). Let's rewrite the equation now.

AB/BC = BC/AC ==> 1 / x = x / (1 + x)

Algebraically rearrange:

1 / x = x / (1 + x) ==> (1 + x) = x

^{2}==> x

^{2}- x - 1

Do you remember basic algebra? We need the quadratic equation to solve for x:

ax

^{2}+ bx + c = 0 ==> x = [-b ± (b

^{2}- 4ac)

^{1/2}] / 2a

Solving for x for x

^{2}+ x - 1 = 0 gives:

x = [-b ± (b

^{2}- 4ac)

^{1/2}] / 2a = [1 ± (-1

^{2}+ 4)

^{1/2}] / 2 = [1 ± (5)

^{1/2}] / 2

The only positive solution is:

x = [1 + (5)

^{1/2}] / 2 = 1.6180339887498948482045868...

It's Phi (F) - the ratio of successive Fibonacci numbers!

This is why F is called the Golden Ratio.

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