If you took a rectangle bounded by the Golden Ratio (meaning, with sides 1.61803...x and x where x is not zero) and cut the biggest square you could make off of it, you'd get a rectangle similar to the original. Basically,
1.618... : 1 = 1 : (1.618... - 1)
Artwork that incorporates the Golden Ratio in its dimensions is known to be 'visually pleasing'.
The inverse of the Golden Ratio is equal to the difference between it and one. The inverse is also equal to is conjugate.
Let's say the Fibonacci sequence is represented by F(x).
F(infinity) / F(infinity-1) = 1.618...
Also,
Which I thought was pretty darn cool.
The Golden Ratio is used by many plants to get more sunlight, as the angle it forms spreads out the most easily.
The Golden Ratio is a root of some simple quadratic functions, like x^2-x-1.
Just thought that was cool.
Stay coolio,
John
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