In the Vol. 29, No. 3, May 1998 issue of "The College Mathematics Journal"
(MAA) (what was once the Two Year College journal as I recall) is a very
interesting article on Daniel Pedoe. I confess my prior ignorance of the name,
but it is a very good, sometimes thought-provoking article, on things like the
purpose of the Ph.D., and the place of geometry in modern mathematics. Prof.
Pedoe is renowned for his work in geometry.
Anyway, the reason I mention this is two things in the artcle, about the
abacus and geometry.
"Using an abacus, Japanese in the 1700s were able to carry out the most
elaborate calculations. The fundamental connection between an integral and its
derivative was not known, and problems on areas, volumes, and so on were
solved by expansions in infinite series and term-by-term calculation. These
methods are described in a recent book by Hidetosi Fukagawa, "Japanese
Mathematical Problems of the Eighteenth and Nineteenth Centuries"."
The geometry I mentioned... Prof. Pedoe worked with a Japanese high school
teacher, the same Hidetosi Fukagawa, who introduced him to 'San Gaku' -
geometrical theorems painted on wooden tablets, which were hung, centuries
ago, in Japanese temples. This caught my eye because the May 1998 issue of
Scientific American has an excellent article entitled "Japanese Temple
Geometry," which deals with the same topic, with many excellent color
illustrations, and references to the same Mr. Fukagawa.
Philip Mahler
Middlesex CC
Bedford, MA
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