I've long known that the Fibonacci numbers are supposed to be found regularly in plants, but today I found a great website that shows exactly where they are found (no math, just pictures). Fibonacci numbers come in a series formed by adding the previous two numbers to get the next one:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
and are beloved of elementary teachers who want some fun numbers to introduce to their students - there are beautiful posters of the series with sunflowers and pineapples to show kids that math can be relevant and fun. I'm not sure how useful it is to know that sunflower seed spirals come in Fibonacci number pairs (e.g. 21, 34), but it's kind of neat. And it makes a nice break from memorizing multiplication tables, even if it is more natural history than math.
The funny thing is that Fibonacci (Leonardo de Pisa, 1170-1250) was one of the greatest mathematicians of the Middle Ages and this series was a minor accomplishment for him. He transmitted much Arabic math to Europe, including the Hindo-Arabic numerals (1-9) and zero, although it took centuries before they came into common use, and introduced the use of the bar in fractions (2/3). He was the first to solve many algebraic problems of the type that terrorize high school students, even though he didn't have decent notation to do so; he did it using base 60 notation, which is really ugly. But now he's known for a simple series of numbers that happen to turn up regularly in nature and taught to 3rd-graders.