Descartes's Lost Theorem
Web resources on Descartes include Rouse Ball's biography, and some of the philosophical texts through Great Books and the George Mason University Classics Dept., and a Mansfield University Math and Culture course page. Resources on Euler: a biography by Katerina Kechris of U.C.L.A., a Swarthmore Math Forum project on the Bridges of Koenigsberg. For references on polyhedral curvature see Thomas Banchoff's early research papers.
(Note: Reviews to the papers listed are in MathSciNet, available to subscribers.)
For example, a right prism on a regular hexagonal base has twelve solid angles. Continuing with Descartes's terminology, but converting to degrees for the calculation (one plane right angle = 90 degrees):
This remarkable theorem is not part of the history of mathematics. Descartes's Treatise was never published and lay hidden like a mathematical time capsule for over two hundred years.
In this column I will examine the statement quoted above (``Descartes's Lost Theorem'') and the surrounding material. They give us a look back into the mind of one of the inventors of modern mathematics at the beginning of his career, and they will give us a chance to examine some of the more interesting discoveries of the next two centuries, discoveries that are fundamental to geometry and topology as we know them today and which Descartes's geometric intuition allowed him to anticipate.
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These web essays are designed for those who have already discovered the joys of mathematics as well as for those who may be uncomfortable with mathematics.
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