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

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

4. Tokyo
Kyoto

7. Kiyomizu-dera Temple, Kyoto

10. ema
= votive tablet

17. Tokyo
Kyoto

18. Kamakura

19. Sugimoto-dera
Temple,
Kamakura

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

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

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

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

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

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

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

46. mrcooksfinal.blogspot.com
blog.japancentre.com
ynt.yafjp.org

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

48. 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 …

50. Myojorinji temple, Gifu Prefecture

51. Tokyo
Kyoto

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

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

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

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

67. 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.

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

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

70. 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.

79. Gifu News
18 Jan 2015

85. A modern incarnation: two sangaku from 1989

89. Thank you!