Sangaku
Shibuya, Tokyo
) in 1859.Sangaku or san gaku (Japanese: 算額, lit. 'calculation tablet') are Japanese geometrical problems or theorems on wooden tablets which were placed as offerings at Shinto shrines or Buddhist temples during the Edo period by members of all social classes.
History
Nara
The sangaku were painted in color on wooden tablets (
modernization
that followed the Edo period, but around nine hundred are known to remain.
Fujita Kagen (1765–1821), a Japanese mathematician of prominence, published the first collection of sangaku problems, his Shimpeki Sampo (Mathematical problems Suspended from the Temple) in 1790, and in 1806 a sequel, the Zoku Shimpeki Sampo.
During this period
infinite series
and term-by-term calculation.
Select examples
| rmiddle | rleft | rright |
|---|---|---|
| 1 | 4 | 4 |
| 4 | 9 | 36 |
| 9 | 16 | 144 |
| 16 | 25 | 400 |
| 72 | 200 | 450 |
| 144 | 441 | 784 |
| The six primitive triplets of integer radii up to 1000 | ||
- A typical problem, which is presented on an 1824 tablet in Gunma Prefecture, covers the relationship of three touching circles with a common tangent, a special case of Descartes' theorem. Given the size of the two outer large circles, what is the size of the small circle between them? The answer is:
(See also Ford circle.)
- Soddy's hexlet, thought previously to have been discovered in the west in 1937, had been discovered on a sangaku dating from 1822.
- One sangaku problem from Sawa Masayoshi and other from Jihei Morikawa were solved only recently.[1][2]
See also
- Equal incircles theorem
- Japanese theorem for concyclic polygons
- Japanese theorem for concyclic quadrilaterals
- Problem of Apollonius
- Recreational mathematics
- Seki Takakazu
Notes
- arXiv:2008.00922 [math.HO].
- ^ Kinoshita, Hiroshi (2018). "An Unsolved Problem in the Yamaguchi's Travell Diary" (PDF). Sangaku Journal of Mathematics. 2: 43–53.
References
- Fukagawa, Hidetoshi, and ISBN 9780919611214; OCLC 474564475
- __________ and Dan Pedoe. (1991) How to resolve Japanese temple geometry problems? (日本の幾何ー何題解けますか?, Nihon no kika nan dai tokemasu ka) Tōkyō : Mori Kitashuppan. ISBN 9784627015302; OCLC 47500620
- __________ and ISBN 069112745X; OCLC 181142099
- Huvent, Géry. (2008). Sangaku. Le mystère des énigmes géométriques japonaises. Paris: Dunod. ISBN 9782100520305; OCLC 470626755
- Rehmeyer, Julie, "Sacred Geometry", Science News, March 21, 2008.
- Rothman, Tony; Fugakawa, Hidetoshi (May 1998). "Japanese Temple Geometry". Scientific American. pp. 84–91.
External links
Wikimedia Commons has media related to Sangaku.
- Sangaku (Japanese votive tablets featuring mathematical puzzles)
- Japanese Temple Geometry Problem
- Sangaku: Reflections on the Phenomenon
- Sangaku Journal of Mathematics
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