# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Japanese Temple Geometry," by Tony Rothman,with cooperation of Hidetoshi Fukagawa. *Scientific American*, May 1998.

During Japan's period of national seclusion (1639-1854) there arosea tradition known as *sangaku*, Japanese temple geometry. Under the roofs of their religious shrines and temples,* sangaku* devotees would hang brightly colored tablets engraved with solutions to geometry problems.

While many of these problems could be solved with ordinary Eulideangeometry, others demanded more complicated mathematics. In fact,many *sangaku* problems required calculus, and Japanese mathematiciansdeveloped a crude form of it in the late 1600s, independently fromtheir Western peers. The most difficult exercises are nearly impossible;today, modern geometers would use advanced techniques such as affine transformations to tackle them.

While mathematically interesting, *sangaku's* cultural aspects could beeven more intriguing. No one knows who began the tradition or why, but it is clear that followers created these tablets as acts of religious homage, and as challenges to other worshippers. *Sangaku* stands out as a distinctive Japanese tradition, and the tablets that have survived are regarded as elegant, beautiful works of art.

*--Ben Stein*