Japanese Mathematics

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/