Following on from what
mblase said: You can draw a series of squares inside a 'golden ratio rectangle' that theoretically goes on forever. If you keep turning the paper
clockwise, and then always draw the square on the left, you can then draw a
spiral through the
diagonally opposite corners of the squares. This is known as the
golden spiral.
+--------------+--------+
| | |
| | |
| | |
| | |
| +-++-----+
| +-++ |
| | | |
+--------------+--+-----+
^
Start here.
This particular spiral is yet another example of the golden ratio in
nature; many of the most attractive
seashells describe this shape.
Although, let me offer a disclaimer here; just because a fair amount of natural shapes fit the golden ratio, this does not give it some kind of magical or religious significance. It could well be that a lot of seashells adopt the 'golden ratio spiral' simply because it is the easiest to build - after all, DNA is known to often create things with a fractal or recursive nature, and the golden ratio is recursive by definition.
Still, a lot of things need to be learnt about the golden ratio. Why do we find it so attractive? Is it because our faces, too, fit this ratio? (With our eyebrows and chin forming the square within the recangle, might I add). Or is this just coincedence? Don't expect an answer anytime soon...