cut-the-knot.org
Sangaku: Reflections on the Phenomenon
(E?)(L?) http://www.cut-the-knot.org/pythagoras/Sangaku.shtml
Sangaku are often colorful tablets offered in shinto shrines (and sometimes in buddhist temples) in Japan and posing mathematical problems. The earliest sangaku date a few years before the beginning of the japanese Edo period (1603-1867) of self-imposed seclusion from the Western world. Most of the write-ups on the Sangaku phenomenon are based on either a Scientific American article by Tony Rothman written in co-operation with Hidetoshi Fukagawa, a Japanese teacher with a Ph.D in mathematics, or the book by H. Fukagawa and D. Pedoe. For example, Rothman explains in the introduction to his article:
...
Sangaku
- Sangaku: Reflections on the Phenomenon
- Critique of My View and a Response
- 1 + 27 = 12 + 16 Sangaku
- 3-4-5 Triangle by a Kid
- 7 = 2 + 5 Sangaku
- A 49th Degree Challenge
- A Geometric Mean Sangaku
- A Hard but Important Sangaku
- A Restored Sangaku Problem
- A better solution to a difficult sangaku problem
- A Trigonometric Solution to a Difficult Sangaku Problem
- A Sangaku: Two Unrelated Circles
- A Sangaku by a Teen
- A Sangaku Follow-Up on an Archimedes' Lemma
- A Sangaku with an Egyptian Attachment
- A Sangaku with Many Circles and Some
- A Sushi Morsel
- An Old Japanese Theorem
- Archimedes Twins in the Edo Period
- Arithmetic Mean Sangaku
- Bottema Shatters Japan's Seclusion
- Chain of Circles on a Chord
- Circles and Semicircles in Rectangle
- Circles in a Circular Segment
- Circles Lined on the Legs of a Right Triangle
- Equal Incircles Theorem
- Equal Incircle Theorem, Angela Drei's Proof
- Equilateral Triangle, Straight Line and Tangent Circles
- Equilateral Triangles and Incircles in a Square
- Five Incircles in a Square
- Four Hinged Squares
- Four Incircles in Equilateral Triangle
- Four Incircles in an Equilateral Triangle, a Sangaku
- Gion Shrine Problem
- Harmonic Mean Sangaku
- Heron's Problem
- In the Wasan Spirit
- Incenters in Cyclic Quadrilateral
- Japanese Art and Mathematics
- Malfatti's Problem
- Maximal Properties of the Pythagorean Relation
- Neuberg Sangaku
- Out of Pentagon Sangaku
- Peacock Tail Sangaku
- Pentagon Proportions Sangaku
- Proportions in Square
- Pythagoras and Vecten Break Japan's Isolation
- Radius of a Circle by Paper Folding
- Review of Sacred Mathematics
- Sangaku à la V. Thebault
- Sangaku and The Egyptian Triangle
- Sangaku in a Square
- Sangaku Iterations, Is it Wasan?
- Sangaku with 8 Circles
- Sangaku with Angle between a Tangent and a Chord
- Sangaku with Quadratic Optimization
- Sangaku with Three Mixtilinear Circles
- Sangaku with Versines
- Sangakus with a Mixtilinear Circle
- Sequences of Touching Circles
- Square and Circle in a Gothic Cupola
- Steiner's Sangaku
- Tangent Circles and an Isosceles Triangle
- The Squinting Eyes Theorem
- Three Incircles In a Right Triangle
- Three Squares and Two Ellipses
- Three Tangent Circles Sangaku
- Triangles, Squares and Areas from Temple Geometry
- Two Arbelos, Two Chains
- Two Circles in an Angle
- Two Sangaku with Equal Incircles
(E?)(L?) http://www.princeton.edu/pr/pwb/06/0605/5a.shtml
...
This wooden sangaku, literally “mathematical tablet,” is one of approximately 900 that survive in Japan from as far back as the 17th century. Sangaku illustrate solutions to puzzles using traditional Japanese geometrical techniques that developed independently of Western methods. Mathematicians frequently hung their often lavishly decorated tablets in temples and shrines as religious offerings. This particular tablet, hung in Fukushima prefecture in 1885, measures 5.6 by 2.4 feet and includes a problem involving a folding fan, a popular item in the 19th century. (Princeton University Press/Asahi Shinbun)
...
Erstellt: 2013-08