Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.
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Transcript of Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.
![Page 1: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/1.jpg)
Mathematics and culture of Kyoto
Patterns and Group theory
Naoki Ohta
![Page 2: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/2.jpg)
1.About roofing tiles in Kyoto
2.About kimonos and patterns in Mannpukuji temple
3.About relation between patterns and group theory
Contents
![Page 3: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/3.jpg)
Japanese roofing tile
![Page 4: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/4.jpg)
Tiles on the roof
Tiles on the roof protect a house from rain, wind and fire.
Some patterns are on these tiles.
![Page 5: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/5.jpg)
The tile of 1300 years ago
Other tiles on the roof
![Page 6: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/6.jpg)
In Shrine and Temple
![Page 7: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/7.jpg)
Houryuji temple in Nara
Glide reflection along the centerline
![Page 8: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/8.jpg)
On kimono
![Page 9: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/9.jpg)
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.
![Page 10: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/10.jpg)
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2. Strip pattern.How many kinds of strip patterns are there?Kinds of strip pattern are seven patterns.
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4. I can’t find the pattern in Kyoto which has rotation by 180 with pole on the centerline.
![Page 12: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/12.jpg)
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Conclusion
Traditional culture in Kyoto include Mathematics!
![Page 14: Mathematics and culture of Kyoto Patterns and Group theory Naoki Ohta.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e5e5503460f94b5701c/html5/thumbnails/14.jpg)
Thank you