Passing on a post from my dad…I think some of the math is accessible for my readers. In fact, for my precalculus students, it ties together some of the nice stuff we’ve studied this semester (infinite series, complex numbers).
Teaching History of Math this past semester gave me an excuse to read carefully two Dover Publications books that I have owned since high school, but only skimmed then. Imagine my delight to discover that if you are given a theorem that is hard to prove beforehand, you can prove that is transcendental in just a couple of lines. The hard theorem gives many other corollaries too, corollaries that I’ve known in my gut but never had a handle on how to prove.
Here are the details, from p. 76 of Felix Klein’s book Famous Problems of Elementary Geometry. You can read it on-line at Google Books.
Go check it out!