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.

In his youth, Coxeter composed music and showed great promise as a pianist. Like many mathematicians, he felt that mathematics and music are intimately related.

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. 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. Returning to Trinity for a year, he attended Ludwig Wittgenstein's seminars on the philosophy of mathematics. In 1934 he spent a further year at Princeton as a Procter Fellow.

In 1936 Coxeter moved to the University of Toronto, becoming a professor in 1948. He was elected a Fellow of the Royal Society of Canada in 1948 and 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 1990, he became a Foreign Member of the American Academy of Arts and Sciences.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

• Boerdijk–Coxeter helix
• Coxeter group
• Coxeter number
• Coxeter–Dynkin diagram
• Coxeter–James Prize
• Coxeter-Todd lattice
• Coxeter's loxodromic sequence of tangent circles
• LCF notation
• Todd-Coxeter algorithm
• Tutte–Coxeter graph

References

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.
• " 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.
• Jaron's World: Shapes in Other Dimensions, Discover mag., Apr 2007
• The Mathematics in the Art of M.C. Escher video of a lecture by H.S.M. Coxeter, April 28, 2000.
• HAROLD SCOTT MACDONALD COXETER 9 February 1907 -- 31 March 2003 by Siobhan Roberts and Asia Ivić Weiss] in Biographical Memoirs of Fellows of the Royal Society (1955-2000), Volume 52 / December 2006.
  • Harold Scott MacDonald Coxeter Bibliography Electronic Supplementary Material to the Royal Society obituary.