Mathematics and culture of Kyoto

Patterns and Group theory

Naoki Ohta

1.About roofing tiles in Kyoto

2.About kimonos and patterns in Mannpukuji temple

3.About relation between patterns and group theory

Contents

Japanese roofing tile

Tiles on the roof

Tiles on the roof protect a house from rain, wind and fire.

Some patterns are on these tiles.

The tile of 1300 years ago

Other tiles on the roof

In Shrine and Temple

Houryuji temple in Nara

Glide reflection along the centerline

On kimono

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.

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.

5.

6.

7.

Conclusion

Traditional culture in Kyoto include Mathematics!

Thank you