The Right Coast

February 17, 2004
Spend all day doing little math puzzles
By Tom Smith

It's good for you. Really.

UPDATE: Here's a famous one some of you may recognize. Consider "triangular numbers." They go, 1, 3, 6, 10, 15 . . . Note that the pattern is 1, 1+2, 1+2+3, 1+2+3+4, and so on. They're triangular because they are the number of dots that can be put in a triangular, bowling pin type pattern. The sum of all triangular numbers is obviously infinite. But what is the sum of the reciprocals of these numbers, i.e., 1/1 + 1/3 + 1/6 + 1/10 . . . Huygens gave this problem to Leibnitz to solve, and he came up with a very clever solution (he was a genius, after all). Supposedly contemplating it and similar problems led him to discover calculus. I showed it to my middle boy, Patrick, and the solution and said "isn't it weird and beautiful?" He said, "more weird than beautiful."