Mathematics and culture of Kyoto

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Mathematics and culture of Kyoto

• Patterns and Group theory
• Naoki Ohta

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Contents

• About roofing tiles in Kyoto
• About kimonos and patterns in
  Mannpukuji temple
• About relation between patterns and group theory

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Japanese roofing tile
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Tiles on the roof

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

Some patterns are on these tiles.
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Other tiles on the roof
The tile of 1300 years ago
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In Shrine and Temple
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Houryuji temple in Nara
Glide reflection along the centerline
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On kimono
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1. Rectangle patterns.
How many kinds of rectangle patterns are there?
Kinds of Rectangle patterns are five patterns.
But I cant find this pattern in Kyoto.
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(No Transcript)
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2. Strip pattern.
How many kinds of strip patterns are there?
Kinds of strip pattern are seven patterns.
1. 2. 3. 4.
I cant find the pattern in Kyoto which has
rotation by 180 with pole on the centerline.
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5.
6. 7.
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Conclusion

• Traditional culture in Kyoto include Mathematics!

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Thank you