1. Traditional Japanese Geometry. SANGAKU.
　算　　　額
　SAN GAKU
Traditional
Japanese Geometry.
SANGAKU.

2. 　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. 　

3. SAN and GAKU implies Mathematics and Tablet, respectively
　SAN and GAKU implies 　Mathematics and Tablet, 　respectively. 　Now, about 900 SANGAKU 　have survived. 　

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

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

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

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

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

9. Sangaku: Art and Mathematics.
Art
Mathematics

10. 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 . .

11. SANGAKU Exhibition, 4/26-6/26, 2005.
Held in Nagoya-city Science Museum.
Editorial supervisor was Fukagawa Hidetoshi
Supported by Asahi-newspaper-company

12. How much money need for this exhibition ?
Do you think ?
How much money need for this exhibition ?
The fare; about USD,
Big money

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

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

15. 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.

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

17. Mathematician of TJM Moko Kitagawa ( ） 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.

18. Replica Sangaku reproduced by Atuta shrine in Nagoya city
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 𝑎 𝑐 = 1 𝑏 𝑑 .

22. Replica Sangaku of Atsuta shrine in Nagoya city
Replica Sangaku of Atsuta shrine in Nagoya city. This tablet was hung in 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.

23. Here is Mathematics problems
Teacher is teaching “Solve
the high degree equation”
to his friends.
People are discussing to do “SANGI”
Women and Boys are
trainng to handle soroban
Sneeze. He seems getting a cold.
Ordinary people enjoyed TJM. In the SANGAKU (1861), two ladies were enjoying TJM. The size is the width 170cm and the height 93cm.

24. When a Rich trader ｅｎｄed 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. 　

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

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

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

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

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

30. 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.

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

32. 終 THE END