算　　　額　 SAN GAKU

Traditional Japanese Geometry.

SANGAKU.

　

　 In 17 century, the Traditional Japanese　 Mathematics started and developed all over Japan.

　 From 17th century to 20th century, many Japanese 　 people enjoyed traditional Japanese mathematics.

　 Some of them wanted to display his ability to the 　 other people and they dedicated wooden tablets 　 to shrines and temples on which mathematics　 problems were drawn.

　 This tablet is called as SANGAKU.

　 　 SAN and GAKU implies 　 Mathematics and Tablet, 　 respectively.

　 Now, about 900 SANGAKU　 have survived.

　 The size of the tablet is width 577cm & Height 　 91cm on which 23 problems were drawn. 　 This tablet is so damaged, hung in 1881.

　 This big Sangaku of 1893 is no damaged since 　 the tablet was hung inside of the temple. 　 The size is width 368cm×height 114cm.

The sangaku is hanging in the shrine and so beautiful. The size is 173cm width and 82cm height, hung in 1854 ．

This shrine is very small and there is no one. Inside of this shrine, the ceiling is so beautiful lattices.

The size of the lattice is 45cm by 45 cm.Fukagawa took the picture in face up.

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Art

Mathematics

Sangaku: Art and Mathematics

In the same shrine another ceiling panel has a beautiful painting along with the mathematical problem. This is a good example of “Art and Mathematics”. The snake entwining the tree is “Art” and the writing in Japanese below it is “Mathematics”. The problem stated here is;A snake of the length 2 meter is sleeping in form of a circumference with the diameter. Then, find the diameter .

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Supported by Asahi-newspaper-company

SANGAKU Exhibition, 4/26-6/26, 2005.Held in Nagoya-city Science Museum.

Editorial supervisor was Fukagawa Hidetoshi

The fare; about 300000 USD, Big money

Do you think ? How much money need for this exhibition ?

Big size Sangaku ：４５３ cm× １５１ cm, in Yamagata.

Largest sangaku in Japan. ６２０ cm× １４０ cm. 　 On this tablet, twenty two problems are written.

About thirty years ago, I visited this shrine to take photos of the biggest SANGAKU in Fukushima. I wanted to introduce it in this conference. The shrine is far from my home.

　 Replica sangaku reproduced by Atsuta 　 shrine was hung in 1806. The width is　 45cm and the height 30cm. In general　 case, Sangaku is challenging to visitors.　 Can you solve ?

Mathematician of TJM Moko Kitagawa (1763-1833 ） visited this shrine, recorded the problem and wrote his solution to the problem in his notebook which is extant. Following is two pages of his old notebook.

Replica Sangaku reproduced by Atuta shrine in Nagoya city. This tablet was hung in １８４１ . The size is the width 45cm and the height 30cm. Find the relation on four circles..... Can you solve ? Result is

Replica Sangaku of Atsuta shrine in Nagoya city. This tablet was hung in 1844. The size is the width 240cm and the height 60cm. Big size. Third problem from the right side is the same one on University Calculus course in Modern age. In general, sangaku problems are difficult.

Ordinary people enjoyed TJM. In the SANGAKU (1861), two ladies were enjoying TJM. The size is the width 170cm and the height 93cm.

Teacher is teaching “Solve the high degree equation” to his friends.

Women and Boys are trainng to handle soroban

People are discussing to do “SANGI”

Here is Mathematics problems

Sneeze. He seems getting a cold.

When a Rich trader ｅｎｄ ed his business work, He decided to learn “Mathematics” and “Poem” as his pastimes. And so he, right side, invited a Mathematician, left side. This is “Solving high degree equation” by means of “SANGI”. This aged rich trader dedicated the following sangaku to shrine. 　

This tablet is so beautiful, hung in 1873. The size is 162cm by 88cm. The frame is good art.

Dragon

Replica of 1813 sangaku by pottery.This problem is on an ellipse and three circles.

Sangaku was lost but the wooden model on this problem is found, at first, by Fukagawa in Meiji Yousui Museum.

This SANGAKU is the smallest in Japan and hung in 1779 at Rokusyo shrine of Aichi. The size is 50cm×25cm.

This is Rokusyo shrine in which the most small sangaku was hung in 1779.It is extant.

Japanese Temple Geometry, Sangaku is an interesting world of mathematics and art. This world developed by ordinary people, including mathematicians, who were love in mathematics, in 17th century to 20th century of Japan.

“Enjoy” is very important in mathematics. This world is useful in mathematics education, I believe. Many thanks for my talk. Hidetoshi Fukagawa.

終THE END