1. Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta

2. 1.About roofing tiles in Kyoto 2.About kimonos and patterns in Mannpukuji temple 3.About relation between patterns and group theory Contents

3. Japanese roofing tile

4. Tiles on the roof Tiles on the roof protect a house from rain, wind and fire. Some patterns are on these tiles.

5. The tile of 1300 years ago Other tiles on the roof

6. In Shrine and Temple

7. Houryuji temple in Nara Glide reflection along the centerline

8. On kimono

9. 1. Rectangle patterns. How many kinds of rectangle patterns are there? Kinds of Rectangle patterns are five patterns. But I can’t find this pattern in Kyoto.

11. 2. Strip pattern. How many kinds of strip patterns are there? Kinds of strip pattern are seven patterns. 1. 2. 3. 4. I can’t find the pattern in Kyoto which has rotation by 180 with pole on the centerline.

12. 5. 6. 7.

13. Conclusion  Traditional culture in Kyoto include Mathematics!

14. Thank you