Sangaku

In a previous post, I talked about the Sangaku of Japan.

http://mikeintaipei.blogspot.com/2011/12/sanguke-in-kyoto.html

These were the geometric problems worked on my Japanese mathematician during the Tokugawa isolationist period. Many of their problems had to do with the area of different configurations of squares, triangles, circles, ... I think that fascination with geometric designs is still with us. Especially in Taiwan, because tiles are so often used. Here are some that caught my eye.

This old advertisement for Nikon cameras uses the design from a sangaku problem.

There is a popular proof of the Pythagorean Theorem based on the inner two squares and triangles of this diagram.

But the problems can have more and more components making the problem more and more complicated.

And this is the floor of the Taipei Train Station.