Sangaku - Citizendia

Sangaku or San Gaku (算額; lit. mathematical tablet) are Japanese geometrical puzzles in Euclidean geometry on wooden tablets created during the Edo period (1603-1867) by members of all social classes. Euclidean geometry is a mathematical system attributed to the Greek Mathematician Euclid of Alexandria. The, also referred to as the Tokugawa period (徳川時代 Tokugawa-jidai) is a division of Japanese history running from 1603 to 1868 The Dutch Japanologist Isaac Titsingh first introduced sangaku to the West when he returned to Europe in the late 1790s after more than twenty years in the Far East. Isaac Titsingh ( 10 January 1745 in Amsterdam – 2 February 1812 in Paris) was a Dutch surgeon scholar merchant-trader ^[1][1]

During this period Japan was completely isolated from the rest of the world so the tablets were created using Japanese mathematics, (wasan), not influenced by western mathematical thought. For a topic outline on this subject see List of basic Japan topics. In the History of mathematics, Japanese mathematics or wasan (和算 denotes a genuinely distinct kind of mathematics developed in Japan during the In the History of mathematics, Japanese mathematics or wasan (和算 denotes a genuinely distinct kind of mathematics developed in Japan during the For example, the fundamental connection between an integral and its derivative was unknown so Sangaku problems on areas and volumes were solved by expansions in infinite series and term-by-term calculation. In Mathematics, a series is often represented as the sum of a Sequence of terms That is a series is represented as a list of numbers with

The Sangaku were painted in color on wooden tablets which were hung in the precincts of Buddhist temples and Shinto shrines as offerings to the gods or as challenges to the congregants. Many of these tablets were lost during the period of modernization that followed the Edo period, but around nine hundred are known to remain. The idea of modernization comes from a view of societies as having a standard Evolutionary pattern as described in the Social evolutionism theories

Sangaku puzzle in which three circles share a tangent.

A typical problem, which is presented on an 1824 tablet in the Gunma Prefecture, covers the relationship of three touching circles with a common tangent. Year 1824 ( MDCCCXXIV) was a Leap year starting on Thursday (link will display the full calendar of the Gregorian Calendar (or a Leap year WikipediaWikiProject Japanese prefectures for guidelines --> is a prefecture of Japan located in the northwest corner of the Kantō region on For the tangent function see Trigonometric functions. For other uses see Tangent (disambiguation. Given the size of the two outer large circles, what is the size of the small circle between then? The answer is:

$\frac{1}{\sqrt{r_{middle}}} = \frac{1}{\sqrt{r_{left}}} + \frac{1}{\sqrt{r_{right}}}$

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.

In recent times, a Sangaku collection was published in 1989 by Hidetoshi Fukagawa and Daniel Pedoe in the book Japanese Temple Geometry Problems. Dan Pedoe (1910&ndash1998 was an English-born mathematician and Geometer with a career spanning more than sixty years

References

^ Association of American Geographers. (1911). Annals of the Association of American Geographers, (Vol. I) p. 35.

Association of American Geographers. Annals of the Association of American Geographers, Vol. I, 1911.
Fukagawa, Hidetoshi and Daniel Pedoe. Japanese Temple Geometry Problems: Sangaku. Charles Babbage Research Centre, 1989. ISBN 0-919611-21-4.
Rothman, Tony and Fugakawa, Hidetoshi. "Japanese Temple Geometry," Scientific American, May 1998.

External links

Sangaku problem by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
http://www.sangaku.info/
http://www.wasan.jp/english/
http://www.loyola.edu/maru/sangaku.html
An interesting Sangaku problem by Archimedes Laboratory
http://www2.gol.com/users/coynerhm/0598rothman.html
Pythagoras and Vecten Break Japan's Isolation

http://matcmadison.edu/is/as/math/kmirus/Reference/SanGaku.html
Sangaku: Reflections on the Phenomenon
East Asia Institute, University of Cambridge: Further reading/bibliography

or (born 1637/1642? – October 24, 1708) was a Japanese Mathematician who created a new algebraic notation system and laid In Geometry, the Japanese theorem states that no matter how we triangulate a Concyclic Polygon, the Sum of inradii of The Japanese theorem states that the centers of the Incircles of certain Triangles inside a Concyclic Quadrilateral are vertices of a rectangle In Geometry, the equal incircles theorem derives from a Japanese Sangaku, and pertains to the following construction a series of rays are drawn from a given point The University of Cambridge (often Cambridge University) located in Cambridge, England, is the second-oldest university in the

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