Date: 02/15/2001 at 15:03:53 From: Kimberly Resendez Subject: Japanese Mathematics I am a pre-service teacher at Tarleton State University, and I have to do a presentation on Japanese mathematics. Do you know of any resources that I can use to find information on my topic? I looked in the archives and found an article about Kumon math, but I would like to have more information on the general subject of Japanese mathematics. Can you offer any suggestions or ideas?
Date: 02/17/2001 at 09:42:11 From: Doctor Jordi Subject: Re: Japanese Mathematics Hello, Kimberly. Thanks for writing to Dr. Math. I'm not really sure what you want to know about Japanese mathematics. If you want to know about modern teaching trends there, the article you already found is a great starting point and has numerous references itself which must be in turn cross-referenced themselves. It's here: Kumon Math http://mathforum.org/dr.math/problems/boyer3.24.96.html If you want to know about the history of mathematics in Japan, here is a page from the MacTutor Math History archives that may help you: References for Takakazu Seki http://www-groups.dcs.st-andrews.ac.uk/~history/References/Seki.html I found it by looking for the keywords 'seki takakazu' in the Google search engine. Seki Takakazu is probably the most famous Japanese mathematician, but he is by no means the only one. The following four books are from a recommended reading list for a course I took at McGill which was partially concerned with Japanese mathematics. You should be able to find information about other mathematicians in them, but I am not sure how available they are to you. Fukagawa, Hidetoshi, and Dan Pedoe. Japanese temple geometry problems. Winnipeg, MB.: Charles Babbage Research Centre, 1989. Horiuchi, Annick. Les mathematiques japonaises a l'epoque d'Edo (1600-1868). Paris: Librairie philosophique J. Vrin, 1994, 409 pp. Mikami, Yoshio. The Development of Mathematics in China and Japan. New York: G. E. Stechert and Co., 1913. Reprinted New York: Chelsea Publishing Co., 1961. Mikami, Yoshio, and D. E. Smith. History of Japanese Mathematics. Chicago: The Open Court Publishing Co., 1914. Here's the link to my reading list: Reading, History and Philosophy of Mathematics http://euclid.math.mcgill.ca/volkov/Reading.html You may also want to learn about the following topics: wasan (literally, "Japanese counting" or "mathematics the Japanese way"), idai (a tradition of handing down unsolved problems to later generations), and the role of calendar-making. The computational devices of the Japanese, i.e. counting rods and later the abacus, should be also points of interest for developing a presentation. Famous mathematicians that you might want to research are: * Mori Shigeyoshi Wrote "Warizansho." (Literally, "japanese division.") * Yoshida Mitsuyoshi A student of Mori, wrote "Jinkoki," a very popular book. He used the abacus in his work (which indicates a loss of the tradition of the counting rods) and probably started the tradition of the idai. * Imamura Tomoaki Another student of Mori, who wrote "Jugairoku." This was not a popular book. * Muramatsu Shigekiyo. Wrote "Sanso." Had interesting ideas about something similar to numerical integration and pi which closely followed the Chinese tradition (much of the Japanese mathematical tradition was completely parallel to the Chinese and did not separate until perhaps only a few centuries ago) and also gave idai of his own. * Sawaguchi Kazuyuki Wrote "Kokos Sanpoki." Gave idai of his own and solved a few given by previous mathematicians. And of course, make sure to research Seki Takakazu and his somewhat controversial book "Hatsubi Sanpo," where he solved ALL 15 idai of Sawaguchi, although some debate arises as to whether he really solved anything at all (like us here at Dr. Math, Seki did not like to give final answers but instead just pointed out the procedure that would lead to a solution). Other points to notice about Japanese mathematics would be the schooling system (the traditional one), the notational devices used for their mathematics (there is something very original and novel about the Japanese notation compared with previous Chinese notation), the rivalries between the Kyoto and Edo (modern Tokyo) schools, and the relationships between teachers and students (in particular, try to find out about an episode in which two students of Seki, the Takebes, defended him passionately against accusations of giving incorrect or incomplete solutions to the idai of Sawaguchi). I hope all this helps. Make sure to research all of these on your own, and if you need more help looking for resources, want to talk about anything more, or have any other questions of whatever kind, you're welcome to write back. - Doctor Jordi, The Math Forum http://mathforum.org/dr.math/
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