The Info List - Coxeter

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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 adult life in Canada. He was always called Donald, from his third name MacDonald.[3] 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.[4]


1 Biography 2 Awards 3 Works 4 See also 5 References 6 Further reading 7 External links

Biography[edit] 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 "Mathematics and Music" in the Canadian Music Journal.[5] Coxeter went up to Trinity College, Cambridge
Trinity College, Cambridge
in 1926 to read mathematics. There he earned his BA (as Senior Wrangler) in 1928, and his doctorate in 1931.[5][3] 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.[3] 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.[3] In 1936 Coxeter moved to the University of Toronto. In 1938 he and P. Du Val, H.T. Flather, and John Flinders Petrie
John Flinders Petrie
published The Fifty-Nine Icosahedra with University of Toronto
University of Toronto
Press. In 1940 Coxeter edited the eleventh edition of Mathematical Recreations and Essays,[6] originally published by W. W. Rouse Ball
W. W. Rouse Ball
in 1892. He was elevated to professor in 1948. Coxeter was elected a Fellow of the Royal Society of Canada
in 1948 and a Fellow of the Royal Society
Fellow of the Royal Society
in 1950. He met Maurits 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.[3] Coxeter, M. S. Longuet-Higgins and J. C. P. Miller were the first to publish the full list of uniform polyhedra (1954).[7] He worked for 60 years at the University of Toronto
University of Toronto
and published twelve books. Awards[edit] Since 1978, the Canadian Mathematical Society have awarded the Coxeter–James Prize in his honor. He was made a Fellow of the Royal Society
Fellow of the Royal Society
in 1950 and in 1997 he was awarded their Sylvester Medal.[3] In 1990, he became a Foreign Member of the American Academy of Arts and Sciences[8] and in 1997 was made a Companion of the Order of Canada.[9] In 1973 he received the Jeffery–Williams Prize.[3] Works[edit]

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),[10] (2nd ed, 1947), (3rd ed, 1957), (4th ed, 1961), (5th ed, 1965), University of Toronto
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
Philosophical Transactions of the Royal Society A
246: 401–50 doi:10.1098/rsta.1954.0003 1949: The Real Projective Plane[11] 1957: (with W.O.J. Moser) Generators and Relations for Discrete Groups[12] 1980: Second edition, Springer-Verlag ISBN 0-387-09212-9 1961: Introduction to Geometry[13][14] 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
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]

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


^ Harold Scott MacDonald Coxeter
Harold Scott MacDonald Coxeter
at the Mathematics Genealogy Project ^ Roberts, S.; Ivic Weiss, A. (2006). "Harold Scott MacDonald Coxeter. 9 February 1907 – 31 March 2003: Elected FRS 1950". Biographical Memoirs of Fellows of the Royal Society. 52: 45–66. doi:10.1098/rsbm.2006.0004.  ^ a b c d e f g O'Connor, John J.; Robertson, Edmund F., "Harold Scott MacDonald Coxeter", MacTutor History of Mathematics archive, University of St Andrews . ^ The Boston Globe
The Boston Globe
(September 10, 2006) "Review: The Man Who Saved Geometry
by Siobhan Roberts. "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" ^ 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 ^ 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.  ^ Coxeter 1954 ^ Foreign Honorary Member elected 1990 2016 American Academy of Arts & Sciences ^ Office of the Governor General of Canada. Order of Canada
Order of Canada
citation. Queen's Printer for Canada. Retrieved 26 May 2010 ^ 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. 

Further reading[edit]

Davis, Chandler; Ellers, Erich W, eds. (2006). The Coxeter Legacy: Reflections and Projections. Providence, R.I.: American Mathematical Society. ISBN 978-0-8218-3722-1. OCLC 62282754.  Roberts, Siobhan (2006). King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry. New York: Walker & Company. ISBN 978-0-8027-1499-2. OCLC 71436884. 

External links[edit]

Archival papers held at University of Toronto
University of Toronto
Archives and Records Management Services Harold Scott MacDonald Coxeter
Harold Scott MacDonald Coxeter
at the Mathematics Genealogy Project H. S. M. Coxeter (1907–2003), Erich W. Ellers, Branko Grünbaum, Peter McMullen, Asia Ivic Weiss Notices of the AMS: Volume 50, Number 10. www.donaldcoxeter.com www.math.yorku.ca/dcoxeter webpages dedicated to him (in development) 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.

Authority control

WorldCat Identities VIAF: 95255476 LCCN: n81019969 ISNI: 0000 0001 0859 4550 GND: 118522507 SELIBR: 182370 SUDOC: 028881907 BNF: cb12062548j (data) MGP: 12555 NDL: 00