The book Sacred Mathematics: Japanese Temple Geometry by Fukagawa Hidetoshi and Tony Rothman is the primary source of stories and questions we are going to discuss.
The notes (hand-written notes in Russian) will appear here:
- 1. What is it all about? (Maths in Edo period)
- 2. Chinese foundation of Japanese mathematics
- 3. Chinese questions on proportions and volumes
- 4. Back to Japan: Pythagorean triples
- 5. Tangent circles
- 6. One sangaku puzzle (with rombus and many circles)
- 7. Paper folding questions
- 8. Approximations and continued fractions
- 9. Three questions about regular triangle
- 10. Two questions about regular pentagon (or golden ratio)
- 11. Silver (or Japanese) ratio
- 12. About Dragons...
- 13. Triangular piles of balls
- 14. Kissing circles
- 15. Circles again
- 16. Apollonian packing
- 17. Apollonian packing - and everything!
- 18. Musical Intermezzo
- 19. 3D problems
- 20. More problems in 3D
- 21. More on the spheres
- 22. Inscribed circle
- 23. About hats
Resources:
- 1. Edo Period images of samurai, in The Metropolitan Museum of Art (online collection).
- 2. Chinese fairy tale The weaver (in 40 slides, 1961, in Russian) - and the same in pdf
- 3a. Mathematics in medieval China by V.E. Eremeev (also explains how to use abacus = counting frame and counting rods)
- 3b. More on using counting rods on Wikipedia
- 4a. Pythagorean triples on 3blue1brown
- 4b. Pythagorean Theorem with many proofs on cut-the-knot
- 5. Ford Circles Fractal zoom to 1.0E+15 by Cody Bloemhard
- 7. Paper folding and cutting Sangaku on cut-the-knot (and other paperfolding geometry)
- 9. Sangaku flexagon template on flexagon.net
- 10. Sangaku Problems on cut-the-knot
- 12a. Japanese Dragons Lesson 27 of Dragonology by Elena elk
- 12b. Dragon Curves Revisited by Sergei Tabachnikov (in THE MATHEMATICAL INTELLIGENCER)
- 12c. Dragon Curves on Wikipedia (with pictures and animations)
- 12d. Chinese Lullaby from "World Lullabies"
- 14. Translation into Russion (and the original) of "The Kiss Precise" (Soddy-Gosset generalisation of Descartes Circle Theorem)
- 16. Looking Through Apollonian Window by Jerzy Kocik
- 17. Golden Satelite in Apollonian Window by Jerzy Kocik
- 18a. Eulers Tonnetz on Wikipedia
- 18b. On-line piano
- 21. From Sangaku Problems to Mathematical Beading, Kazunori Horibea, Bih-Yaw Jinb and Chia-Chin Tsoo.
- 22. The Snow Queen, by Evgeny Schwarz (in Russian)
Hiroshi Kotera collected several hundreds of images of sangaku tables - out of about 820 that survived (click on hieroglyphs to see the pictures!). The English version of the page contains the map of prefectures in Japan.
Geometry Textbook:
- Geometry textbook by O. V. Pogorelov: in Ukranian and in Russian.
Links to 2022/23 pages:
Geometry Around us How to Solve it - and - Geometry in Figures Mathematics and Art
Geometry Around us How to Solve it - and - Geometry in Figures Mathematics and Art