*Geometry*. After finding a proof with the aid of Geometer's Sketchpad I happened to discover through Wikipedia that the theorem has a name: The Japanese Theorem For Quadrilaterals. Then Peter Renz, one of Jacobs' editors, suggested I look at the book

*Sacred Geometry: Japanese Temple Geometry*by Fukagawa Hidetoshi and Tony Rothman, which allowed me to place the theorem in a rich cultural and mathematical context.

The talk is at http://www.scribd.com/doc/129968316/NES-MAA-Presentation. This consists of the slides that I used, put in portrait page orientation, but otherwise unchanged. It is a bit terse, but I hope some find it interesting.