One of the most awe inspiring things that I was ever told about Fibonacci numbers was in relation to pine cones. Take a random pine cone off the ground. (It works better if it's a big hard one (I'm in math, not biology, excuse me) Then look at the bottom. There will be 2 sets of spirals on the bottom that look somewhat like fan blades, one going to the left, the other set going to the right. Count each spiral for each direction. The 2 numbers you get will always be sequential Fibonacci numbers. My professor said he had be doing this for years, and had never found one larger than a 13,21 (first spiral had 13, second had 21) pine cone. If we found a 21,34 cone he would buy it from us, he said. Pretty interesting, no?

See logarithmic spiral for a bit of an explanation for this.