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( R e d i r e c t e d f r o m H . S . M . C o x e t e r )
Canadian geometer (1907–2003)
Harold Scott MacDonald "Donald " Coxeter CC FRS FRSC (9 February 1907 – 31 March 2003)[2] was a British-Canadian geometer and mathematician. He is regarded as one of the greatest geometers of the 20th century.[3]
Coxeter was born in England and educated at the University of Cambridge , with student visits to Princeton University . He worked for 60 years at the University of Toronto in Canada, from 1936 until his retirement in 1996, becoming a full professor there in 1948. His many honours included membership in the Royal Society of Canada , the Royal Society , and the Order of Canada .
He was an author of 12 books, including The Fifty-Nine Icosahedra (1938) and Regular Polytopes (1947). Many concepts in geometry and group theory are named after him, including the Coxeter graph , Coxeter groups , Coxeter's loxodromic sequence of tangent circles , Coxeter–Dynkin diagrams , and the Todd–Coxeter algorithm .
Biography [ edit ]
Coxeter was born in Kensington , England, to Harold Samuel Coxeter and Lucy (née Gee ). His father had taken over the family business of Coxeter & Son, manufacturers of surgical instruments and compressed gases (including a mechanism for anaesthetising surgical patients with nitrous oxide ), but was able to retire early and focus on sculpting and baritone singing; Lucy Coxeter was a portrait and landscape painter who had attended the Royal Academy of Arts . A maternal cousin was the architect Sir Giles Gilbert Scott .[4] [2]
In his youth, Coxeter composed music and was an accomplished pianist at the age of 10.[5] He felt that mathematics and music were intimately related, outlining his ideas in a 1962 article on "Music and Mathematics" in the Canadian Music Journal .[5]
He was educated at King Alfred School, London , and St George's School, Harpenden , where his best friend was John Flinders Petrie, later a mathematician for whom Petrie polygons were named. He was accepted at King's College, Cambridge , in 1925, but decided to spend a year studying in hopes of gaining admittance to Trinity College , where the standard of mathematics was higher.[2] Coxeter won an entrance scholarship and went to Trinity in 1926 to read mathematics. There he earned his BA (as Senior Wrangler ) in 1928, and his doctorate in 1931.[5] [6] 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 .[6] Returning to Trinity for a year, he attended Ludwig Wittgenstein 's seminars on the philosophy of mathematics .[5] In 1934 he spent a further year at Princeton as a Procter Fellow.[6]
In 1936 Coxeter moved to the University of Toronto. In 1938 he and P. Du Val , H. T. Flather, and John Flinders Petrie published The Fifty-Nine Icosahedra with University of Toronto Press . In 1940 Coxeter edited the eleventh edition of Mathematical Recreations and Essays ,[7] originally published by W. W. Rouse Ball in 1892. He was elevated to 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 M. C. Escher in 1954 and the two became lifelong friends; 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 .[6] Coxeter, M. S. Longuet-Higgins and J. C. P. Miller were the first to publish the full list of uniform polyhedra (1954).[8]
He worked for 60 years at the University of Toronto and published twelve books.
Personal life [ edit ]
Coxeter was a vegetarian . He attributed his longevity to his vegetarian diet, daily exercise such as fifty press-ups and standing on his head for fifteen minutes each morning, and consuming a nightly cocktail made from Kahlúa , peach schnapps, and soy milk .[4]
Since 1978, the Canadian Mathematical Society have awarded the Coxeter–James Prize in his honor.
He was made a Fellow of the Royal Society in 1950 and in 1997 he was awarded their Sylvester Medal .[6] In 1990, he became a Foreign Member of the American Academy of Arts and Sciences [9] and in 1997 was made a Companion of the Order of Canada .[10]
In 1973 he received the Jeffery–Williams Prize .[6]
A festschrift in his honour, The Geometric Vein , was published in 1982. It contained 41 essays on geometry, based on a symposium for Coxeter held at Toronto in 1979.[11] A second such volume, The Coxeter Legacy , was published in 2006 based on a Toronto Coxeter symposium held in 2004.[12]
1940: "Regular and Semi-Regular Polytopes I" , Mathematische Zeitschrift 46: 380–407, MR 2,10 doi :10.1007/BF01181449
1942: Non-Euclidean Geometry (1st edition),[13] (2nd ed, 1947), (3rd ed, 1957), (4th ed, 1961), (5th ed, 1965), University of Toronto Press (6th ed, 1998), MAA .
1954: (with Michael S. Longuet-Higgins and J. C. P. Miller ) "Uniform Polyhedra", Philosophical Transactions of the Royal Society A 246: 401–50 doi :10.1098/rsta.1954.0003
1949: The Real Projective Plane [14]
1957: (with W. O. J. Moser) Generators and Relations for Discrete Groups [15] 1980: Second edition, Springer-Verlag ISBN 0-387-09212-9
1961: Introduction to Geometry [16] [17]
1963: Regular Polytopes (2nd edition), Macmillan Company
1967: (with S. L. Greitzer ) Geometry Revisited
1970: Twisted honeycombs (American Mathematical Society, 1970, Regional conference series in mathematics Number 4, ISBN 0-8218-1653-5 )
1973: Regular Polytopes , (3rd edition), Dover edition, ISBN 0-486-61480-8
1974: Projective Geometry (2nd edition)
1974: Regular Complex Polytopes , Cambridge University Press
1981: (with R. Frucht and D. L. Powers), Zero-Symmetric Graphs , Academic Press .
1985: "Regular and Semi-Regular Polytopes II" , Mathematische Zeitschrift 188: 559–591
1987 Projective Geometry (1987) ISBN 978-0-387-40623-7
1988: "Regular and Semi-Regular Polytopes III" , Mathematische Zeitschrift 200: 3–45
1995: F. Arthur Sherk, Peter McMullen, Anthony C. Thompson and Asia Ivić Weiss, editors: Kaleidoscopes — Selected Writings of H. S. M. Coxeter . John Wiley and Sons ISBN 0-471-01003-0
1999: The Beauty of Geometry: Twelve Essays , Dover Publications, LCCN 99-35678 , ISBN 0-486-40919-8
See also [ edit ]
References [ edit ]
^ "Geometry Revisited" . Mathematical Association of America . Archived from the original on 25 December 2018. Retrieved 25 December 2018 .
^ a b "Oxford Dictionary of National Biography" . Oxford Dictionary of National Biography (online ed.). Oxford University Press. 2004. doi :10.1093/ref:odnb/89876 . (Subscription or UK public library membership required.)
^ 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
^ a b c d e f O'Connor, John J.; Robertson, Edmund F. , "Harold Scott MacDonald Coxeter" , MacTutor History of Mathematics Archive , University of St Andrews
^ Frame, J. S. (1940). "Review: Mathematical Recreations and Essays , 11th edition, by W. W. Rouse Ball; revised by H. S. M. Coxeter" (PDF) . Bull. Amer. Math. Soc . 45 (3 ): 211–213. doi :10.1090/S0002-9904-1940-07170-8 .
^ Harold Coxeter, Michael S. Longuet-Higgins and J. C. P. Miller . "Uniform Polyhedra", Philosophical Transactions of the Royal Society A 246: 401–50 doi :10.1098/rsta.1954.0003
^ "Harold Scott MacDonald Coxeter" . Member directory . American Academy of Arts and Sciences. Retrieved 7 June 2024 .
^ Office of the Governor General of Canada . Order of Canada citation . Queen's Printer for Canada. Retrieved 26 May 2010
^ Edge, W. L. (June 1983). "Review of The Geometric Vein " . Proceedings of the Edinburgh Mathematical Society . 26 (2 ): 284–285. doi :10.1017/s0013091500017016 .
^ Davis, Chandler; Ellers, Erich, eds. (2006). The Coxeter Legacy . Providence, Rhode Island: American Mathematical Society. ISBN 978-0821837221 .
^ 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 .
^ 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 .
^ Hall Jr., Marshall (1958). "Review: Generators and relations for discrete groups by H. S. M. Coxeter and W. O. J. Moser" (PDF) . Bulletin of the American Mathematical Society . 64, Part 1 (3 ): 106–108. doi :10.1090/S0002-9904-1958-10178-0 .
^ 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 .
^ Levi, H. (1963). "Review: Introduction to Geometry by H. S. M. Coxeter". The Journal of Philosophy . 60 (1 ): 19–21. doi :10.2307/2023059 . JSTOR 2023059 .
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