Harold Scott MacDonald Coxeter

CC FRS FRSC
Born(1907-02-09)9 February 1907
London, England
Died31 March 2003(2003-03-31) (aged 96)
Toronto, Ontario, Canada
Alma materUniversity of Cambridge (B.A., 1929; Ph.D., 1931)
Known forCoxeter element
Coxeter functor
Coxeter graph
Coxeter group
Coxeter matroid
Coxeter notation
Coxeter's loxodromic sequence of tangent circles
Coxeter–Dynkin diagram
Coxeter–Todd lattice
Boerdijk–Coxeter helix
Goldberg–Coxeter construction
Todd–Coxeter algorithm*
Tutte–Coxeter graph
LCF notation
Regular skew apeirohedra
Spouse(s)Hendrina, died in 1999
Childrena daughter, Susan Thomas, and a son, Edgar
Awards
Scientific career
FieldsGeometry
InstitutionsUniversity of Toronto
Doctoral advisorH. F. Baker[1]
Doctoral students

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]

Biography

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

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]

Awards

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]

Works

  • 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

References

  1. ↑ Harold Scott MacDonald Coxeter at the Mathematics Genealogy Project
  2. 1 2 3 Roberts, Siobhan; Ivić Weiss, Asia (2006). Longair, Malcolm (ed.). "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. ISSN 1748-8494.
  3. ↑ "Geometry Revisited". Mathematical Association of America. Archived from the original on 25 December 2018. Retrieved 25 December 2018.
  4. 1 2 "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.)
  5. 1 2 3 4 Roberts, Siobhan, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, Walker & Company, 2006, ISBN 0-8027-1499-4
  6. 1 2 3 4 5 6 O'Connor, John J.; Robertson, Edmund F., "Harold Scott MacDonald Coxeter", MacTutor History of Mathematics Archive, University of St Andrews
  7. ↑ 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.
  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
  9. ↑ Foreign Honorary Member elected 1990 2016 American Academy of Arts & Sciences
  10. ↑ Office of the Governor General of Canada. Order of Canada citation. Queen's Printer for Canada. Retrieved 26 May 2010
  11. ↑ Edge, W. L. (June 1983). "Review of The Geometric Vein". Proceedings of the Edinburgh Mathematical Society. 26 (2): 284–285. doi:10.1017/s0013091500017016.
  12. ↑ Davis, Chandler; Ellers, Erich, eds. (2006). The Coxeter Legacy. Providence, Rhode Island: American Mathematical Society. ISBN 978-0821837221.
  13. ↑ 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.
  14. ↑ 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.
  15. ↑ 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.
  16. ↑ 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.
  17. ↑ 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

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