Harold Scott MacDonald "Donald" Coxeter CC (February 9, 1907 ? March 31, 2003) is regarded as one of the great geometers of the 20th century. He was born in London but spent most of his life in Canada.

He worked for 60 years at the University of Toronto and published twelve books. He was most noted for his work on regular polytopes and higher-dimensional geometries. He was a champion of the classical approach to geometry, in a period when the tendency was to approach geometry more and more via algebra.

Coxeter went up to Trinity College, Cambridge in 1926 to read mathematics. There he earned his BA in 1928, and his doctorate in 1931. ^{[1] [2]} In 1932 he went to Princeton University for a year as a Rockefeller Fellow, where he worked with Hermann Weyl, Oswald Veblen, and Solomon Lefschetz.^[2] Returning to Trinity for a year, he attended Ludwig Wittgenstein's seminars on the philosophy of mathematics.^[1] In 1934 he spent a further year at Princeton as a Procter Fellow.^[2]

In 1936 Coxeter moved to the University of Toronto, becoming a professor in 1948. He was elected a Fellow of the Royal Society in 1950. He met Maurits Escher and his work on geometric figures helped inspire some of Escher's works, particularly the Circle Limit series based on hyperbolic tessellations. He also inspired some of the innovations of Buckminster Fuller.

Coxeter, M. S. Longuet-Higgins and J. C. P. Miller were the first to publish the full list of uniform polyhedra (1954).

Since 1978 the Canadian Mathematical Society awards the Coxeter?James Prize in his honor.

In 1997 he received Sylvester Medal from the Royal Society and was made a Companion of the Order of Canada.

Works

• Coxeter, Longuet-Higgins, Miller, Uniform polyhedra, Phil. Trans. 1954, 246 A, 401?50.
• The Real Projective Plane (1949)
• Introduction to Geometry (1961)
• Regular Polytopes (1963), Macmillian Company
  • Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8
• Non-Euclidean Geometry (1965)
• Geometry Revisited (with S. L. Greitzer, 1967)
• Projective Geometry (2nd edition, 1974)
• Regular Complex Polytopes (1974), Cambridge University Press
• The Beauty of Geometry: Twelve Essays (1999), Dover Publications, , ISBN 0-486-40919-8
• The Fifty-Nine Icosahedra (with P. Du Val, H. T. Flather, J. F. Petrie)
• Mathematical Recreations and Essays (with W. W. Rouse Ball)

See also

• Coxeter?James Prize
• Coxeter group
• Coxeter number
• Todd-Coxeter algorithm
• Coxeter-Todd lattice
• Coxeter?Dynkin diagram
• Coxeter's loxodromic sequence of tangent circles

References

1. ↑ ^{a b} Roberts, Siobhan, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, Walker & Company, 2006, ISBN 0802714994
2. ↑ ^{a b c}

External links

• H. S. M. Coxeter (1907?2003), Erich W. Ellers, Branko Grünbaum, Peter McMullen, Asia Ivic Weiss Notices of the AMS: VOLUME 50, NUMBER 10, PDF
• "The man who saved geometry: Crying `Death to Triangles!' a generation of mathematicians tried to eliminate geometry in favor of algebra. Were it not for Donald Coxeter, they might have succeeded", by Siobhan Roberts, The Boston Globe, September 10, 2006 http://www.boston.com/news/globe/ideas/articles/2006/09/10/the_man_who_saved_geometry?mode=PF
• Jaron's World: Shapes in Other Dimensions, Discover mag., Apr 2007

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