Fenceposts, Benzene, and Euler
These questions came up on a family drive last weekend:

How many posts does a hundredyard fence with oneyard beams have? !/images/2003/fencepostsline.png!

What if the fence is circular?

What if it’s a cross?

What if it’s a figure eight?
The first question illustrates fencepost error. The second relates to the discovery of the benzene ring. And the last leads to Euler’s Formula. These three questions are from three different fields (computer science, chemistry, and math), but they’re all variants of the same question. (Of course that question is mathematical. That’s the point of math.)