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Revision as of 18:47, 10 September 2014

Harold Scott MacDonald Coxeter
File:Coxeter.jpg
Born(1907-02-09)February 9, 1907
London, England
DiedMarch 31, 2003(2003-03-31) (aged 96)
Toronto, Ontario, Canada
Spouse(s)Hendrina, died in 1999
ChildrenSusan Thomas, and a son, Edgar
AwardsHenry Marshall Tory Medal (1949)
CRM-Fields-PIMS prize (1995)
Sylvester Medal (1997)
Scientific career
FieldsGeometry
InstitutionsUniversity of Toronto
Doctoral advisorH. F. Baker[1]
Doctoral studentsNorman Johnson

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, CC (February 9, 1907 – March 31, 2003)[2] was a British-born Canadian geometer. Coxeter is regarded as one of the greatest geometers of the 20th century. He was born in London but spent most of his life in Canada.

Biography

In his youth, Coxeter composed music and was an accomplished pianist at the age of 10.[3] He felt that mathematics and music were intimately related, outlining his ideas in a 1962 article on "Mathematics and Music" in the Canadian Music Journal.[3]

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 (as Senior Wrangler) in 1928, and his doctorate in 1931.[3][4] 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.[4] Returning to Trinity for a year, he attended Ludwig Wittgenstein's seminars on the philosophy of mathematics.[3] In 1934 he spent a further year at Princeton as a Procter Fellow.[4]

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 have awarded 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.[5]

Works

  • Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
  • Coxeter, Longuet-Higgins, Miller, Uniform polyhedra, Phil. Trans. 1954, 246 A, 401–450.
  • The Real Projective Plane (1949)[6]
  • Introduction to Geometry (1961)[7]
  • Regular Polytopes (2nd edition, 1963), Macmillian Company
  • Non-Euclidean Geometry (1st ed, 1942),[8] (2nd ed, 1947), (3rd ed, 1957), (4th ed, 1961), (5th ed, 1965), U. of Toronto Press; (6th ed, 1998), MAA.
  • Geometry Revisited (with S. L. Greitzer, 1967)
  • Twisted honeycombs (American Mathematical Society, 1970, Regional conference series in mathematics Number 4, ISBN 0-8218-1653-5)
  • Projective Geometry (2nd edition, 1974)
  • Regular Complex Polytopes (1974), Cambridge University Press
  • Coxeter, H. S. M. and Moser, W. O. J. (1980). Generators and Relations for Discrete Groups. New York: Springer-Verlag. ISBN 0-387-09212-9.{{cite book}}: CS1 maint: multiple names: authors list (link) (1st ed, 1957)[9]
  • H.S.M. Coxeter, R. Frucht and D. L. Powers, Zero-Symmetric Graphs, (1981) Academic Press.
  • Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
  • Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • F. Arthur Sherk, Peter McMullen, Anthony C. Thompson and Asia Ivić Weiss, editors: Kaleidoscopes — Selected Writings of H.S.M. Coxeter. John Wiley, 1995, ISBN 0-471-01003-0
  • The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, 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)

Bibliography

See also

References

  1. ^ Harold Scott MacDonald Coxeter at the Mathematics Genealogy Project
  2. ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1098/rsbm.2006.0004, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1098/rsbm.2006.0004 instead.
  3. ^ a b c d Roberts, Siobhan, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, Walker & Company, 2006, ISBN 0-8027-1499-4
  4. ^ a b c O'Connor, John J.; Robertson, Edmund F., "Harold Scott MacDonald Coxeter", MacTutor History of Mathematics Archive, University of St Andrews
  5. ^ Office of the Governor General of Canada. Order of Canada citation. Queen's Printer for Canada. Retrieved 26 May 2010
  6. ^ DuVal, Patrick (1950). "Review: The real projective plane by H. S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 56 (4): 376–378. doi:10.1090/s0002-9904-1950-09414-2.
  7. ^ Freudenthal, H. (1962). "Review: Introduction to geometry by H. S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 68 (2): 55–59. doi:10.1090/s0002-9904-1962-10714-9.
  8. ^ Blumenthal, L. M. (1943). "Review: Non-euclidean geometry by H. S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 49 (9): 679–680. doi:10.1090/s0002-9904-1943-07977-3.
  9. ^ Hall Jr., Marshall (1958). "Review: Generators and relations for discrete groups by H. S. M. Coxeter and W. O. J. Moser" (PDF). Bull. Amer. Math. Soc. 64, Part 1 (3): 106–108.

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