The Japanese theorem for nonconvex polygons

A couple of years ago I wrote blog posts about two beautiful theorems from geometry: the so-called Japanese theorem and Carnot’s theorem. Today I finished a draft of a web article that looks at both of these theorems in more detail. It contains all that you could want—connections between these theorems, generalizations of them, and consequence of…

Some LaTeX odds and ends

Here are a few LaTeX tricks I’d like to share. None of them are earth-shattering, but maybe they’d be useful to some of you. (If you want to try these out, you can download this sample tex file and bib file that contains these tricks.) 1. I have always wanted LaTeX to support inline comments. In many…

Extreme examples and counterexamples

I recently read this puzzle at the Futility Closet and it reminded me of a technique that I like to use to test conjectures (when possible). I don’t know if it has a name, so I’ll call it “looking for extreme examples and counterexamples.” I like this technique because when it works it is fast and…