Geometry in 18th Century Japan Exploring and Creating Sangaku David Clark Randolph-Macon College MD-DC-VA Section Meeting November 7, 2015

Find an equation relating the radii of the blue circles. (circa 1788) From Tony Rothman’s “Japanese Temple Geometry,” Scientific American, May 1998.

Tokyo Kyoto www.freeworldmaps.net

Kiyomizu-dera Temple, Kyoto

ema = votive tablet

Tokyo Kyoto www.freeworldmaps.net

Kamakura

Sugimoto-dera Temple, Kamakura

Sangaku = san “mathematical” + gaku “tablet” Posted under the eaves of shrines and temples Meant as offerings to the gods … … and challenges to other worshippers

Find an equation relating the radii of the blue circles. (circa 1788) From Tony Rothman’s “Japanese Temple Geometry,” Scientific American, May 1998.

Find an equation relating the radii of these circles. (1824)

Given the length of the cord and the radius of the small circle, find the radius of the orange circles. (1873)

Given the side of the smallest square, find all other side lengths and radii. (1854)

Show that the blue circles have half the radius of the white circles

Wasan = wa “Japan” + san “mathematics” (18th and 19th centuries) From Fukagawa and Rothman’s Sacred Mathematics: Japanese Temple Geometry, Princeton 2008.

mrcooksfinal.blogspot.com www.wikipedia.org www.wikipedia.org blog.japancentre.com ynt.yafjp.org

Wasan = wa “Japan” + san “mathematics” (18th and 19th centuries) From Fukagawa and Rothman’s Sacred Mathematics: Japanese Temple Geometry, Princeton 2008.

Juku schools, run by samurai, churned out solutions to countless problems like this. High volume, vast geographic spread, lack of technology made “journal-style” scholarship impossible. Authors of theorems needed another outlet for displaying their work …

Myojorinji temple, Gifu Prefecture

Tokyo Kyoto www.freeworldmaps.net

Mizuho shrine Nagano prefecture, 1800 From Fukagawa and Rothman’s Sacred Mathematics: Japanese Temple Geometry, Princeton 2008.

Murahisagun Okayama city, 1873 Katayamahiko shrine Murahisagun Okayama city, 1873 From Fukagawa and Rothman’s Sacred Mathematics: Japanese Temple Geometry, Princeton 2008.

Sugawara Tenman shrine Mie prefecture, 1854 From Fukagawa and Rothman’s Sacred Mathematics: Japanese Temple Geometry, Princeton 2008.

Ubara shrine Toyama prefecture, 1879 From Fukagawa and Rothman’s Sacred Mathematics: Japanese Temple Geometry, Princeton 2008.

Discovered in 1994 at a temple about to be destroyed; posted in 1814 From Fukagawa and Rothman’s Sacred Mathematics: Japanese Temple Geometry, Princeton 2008.

Onnma shrine Aichi prefecture, 1797 From Fukagawa and Rothman’s Sacred Mathematics: Japanese Temple Geometry, Princeton 2008.

Dewasanzan shrine Yamagata prefecture, 1823 From Fukagawa and Rothman’s Sacred Mathematics: Japanese Temple Geometry, Princeton 2008.

About 900 sangaku survive today. This is thought to be about 1 in 10 of the original number produced during the 18th and 19th centuries.

Gifu News 18 Jan 2015

A modern incarnation: two sangaku from 1989

Thank you! davidclark@rmc.edu