## This website follows two topics: Japanese Temple Geometry and Constructive Mathematics. For some more personal stuff, see my Goddard College faculty page.

## Japanese Temple Geometry ...

... refers not to the design of Japanese temples, but to the Euclidean geometry that was practiced in Zen and Shinto temples during the Edo period, when Japan cut itself off from contact with the West. For an more about this unique piece of mathematical history, see my essay Mathematics and War: from Japanese Temple Geometry to Pearl Harbor.

The problems of JTG were painted on wooden panels called

The problems of JTG were painted on wooden panels called

*sangaku*that were hung in temples as objects of contemplation and study. They have inspired me to produce a series of art works that place JTG problems, precisely created with the dynamic geometry program GeoGebra, on backgrounds of trees and bark. A selection from this ongoing project appears in the slideshow Japanese Temple Geometry on Vermont Trees and Bark.## Constructive Mathematics

I was trained in the Platonist faith that mathematics is absolute truth about an external mathematical reality (Ph. D. Princeton, 1961). When I encountered the Constructive Mathematics of Errett Bishop, I lost that faith and came to see mathematics as socially constructed. Here are two papers from that earlier period of my life which still attract some interest:

**was presented at a symposium on Constructivity in Computer Science, held in San Antonio, Texas in June 1991. The proceedings,***Bringing Mathematics Education Into the Algorithmic Age***, were published in 1992 as volume 613 in the Springer-Verlag series Lecture Notes in Computer Science, edited by J. P. Meyers, Jr. and M. J. O'Donnell. While my expectations that an algorithmic revolution was near at hand were absurdly optimistic, the piece otherwise seems to me to stand up rather well. It received glowing responses from quite a few computer scientists but was universally ignored by mathematicians.***Constructivity in Computer Science***is the piece of constructive mathematical research of which I am most fond. It appeared in***Linear Order in Lattices: a Constructive Study***, edited by Gian-Carlo Rota and published ihn 1978 by Academic Press. It investigates, in the axiomatic context of lattice ordered fields, the question:***Studies in Foundations and Combinatorics**are the real numbers (constructively) linearly ordered*? Apparently, 35 years later, the piece is still of interest to some researchers, since academia.edu analytics keeps sending me occasional notices that it has been viewed.