Before we get into the really fun stuff, let's take a minute to talk about some background on this fascinating number: The Golden Ratio.

The Golden Ratio is approximately 1.618, but it can be written exactly as:

I know, that's not a very pretty looking number, but trust me: it does some very pretty things.

I've given you a decimal representation of the number and an exact representation, now let me give you a representation in words: If a and b are two numbers such that a > b, and the ratio R of a tob is the same as the ratio of a + b to a, then R is The Golden Ratio.

Was that confusing? Well, the easiest way to get rid of that confusion is to convert those words to an algebraic expression, and then solve, as shown below.
 

Note: If you were paying close attention through that algebraic mess above, you may have noticed that I left out a negative root to the quadratic equation. This is because The Golden Ratio was originally used with relation to geometric figures and their side ratios, which meant that the negative root was meaningless. But if you noticed that, great job! And I'll come back to the negative root a bit later on in these pages.

The Golden Ratio is considered "special" enough to have its own symbol, just like the number PI (which is also a ratio - the ratio of the circumference to the diameter of a circle). The Golden Ratio is assigned the Greek letter Phi (φ).

Ancient mathematicians, artists, and architects thought that this ratio was the most aesthetically "pleasing" ratio to look at. Thus, when designing buildings or spacing elements in a painting or sculpture, artists would be careful to make use of this number.

But why is everyone so fascinated with this number φ? Well, that's what we'll get into in the next pages! Click Next below to find out more!