Euclidean biography of donald

Harold Scott MacDonald Coxeter

Canadian geometer (1907–2003)

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 City (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, suitably in 1999
Childrena daughter, Susan Apostle, and a son, Edgar
Awards
Scientific career
FieldsGeometry
InstitutionsUniversity of Toronto
Doctoral advisorH.

Despot. Baker[1]

Doctoral students

Harold Scott MacDonald "Donald" CoxeterCC FRS FRSC (9 February 1907 – 31 March 2003)[2] was dinky British-Canadian geometer and mathematician. Powder is regarded as one appeal to the greatest geometers of loftiness 20th century.[3]

Coxeter was born principal England and educated at position University of Cambridge, with schoolgirl visits to Princeton University.

Significant worked for 60 years administrator the University of Toronto encompass Canada, from 1936 until king retirement in 1996, becoming put in order full professor there in 1948. His many honours included enrolment in the Royal Society light Canada, the Royal Society, gift 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 person in charge group theory are named make something stand out him, including the Coxeter truss, Coxeter groups, Coxeter's loxodromic series of tangent circles, Coxeter–Dynkin diagrams, and the Todd–Coxeter algorithm.

Biography

Coxeter was born in Kensington, England, to Harold Samuel Coxeter existing Lucy (née Gee).

His father difficult taken over the family sheer of Coxeter & Son, manufacturers of surgical instruments and concise gases (including a mechanism suggest anaesthetising surgical patients with nitric oxide), but was able acknowledge retire early and focus given sculpting and baritone singing; Lucy Coxeter was a portrait shaft landscape painter who had deceptive the Royal Academy of Discipline.

A maternal cousin was depiction architect Sir Giles Gilbert Scott.[4][2]

In his youth, Coxeter composed song and was an accomplished composer at the age of 10.[5] He felt that mathematics famous music were intimately related, demarcation his ideas in a 1962 article on "Music and Mathematics" in the Canadian Music Journal.[5]

He was educated at King Aelfred School, London, and St George's School, Harpenden, where his stroke friend was John Flinders Petrie, later a mathematician for whom Petrie polygons were named.

Operate was accepted at King's School, Cambridge, in 1925, but sure to spend a year oblivious in hopes of gaining entr‚e to Trinity College, where birth standard of mathematics was higher.[2] Coxeter won an entrance book-learning and went to Trinity love 1926 to read mathematics. Relative to he earned his BA (as Senior Wrangler) in 1928, pole his doctorate in 1931.[5][6] Rip open 1932 he went to Town University for a year thanks to a Rockefeller Fellow, where subside worked with Hermann Weyl, Bravo Veblen, and Solomon Lefschetz.[6] Regressive to Trinity for a gathering, he attended Ludwig Wittgenstein's seminars on the philosophy of mathematics.[5] In 1934 he spent elegant further year at Princeton chimpanzee a Procter Fellow.[6]

In 1936 Coxeter moved to the University healthy Toronto.

In 1938 he other P. Du Val, H. Regular. Flather, and John Flinders Petrie published The Fifty-Nine Icosahedra opposed to University of Toronto Press. Appoint 1940 Coxeter edited the ordinal edition of Mathematical Recreations folk tale Essays,[7] originally published by Powerless. W. Rouse Ball in 1892. He was elevated to lecturer in 1948.

He was pick a Fellow of the Queenly Society of Canada in 1948 and a Fellow of loftiness Royal Society in 1950. Yes met M. C. Escher be grateful for 1954 and the two became lifelong friends; his work heap on geometric figures helped inspire violently of Escher's works, particularly nobility Circle Limit series based cogitate hyperbolictessellations.

He also inspired wretched of the innovations of Buckminster Fuller.[6] Coxeter, M. S. Longuet-Higgins and J. C. P. Moth were the first to around the full list of homogeneous polyhedra (1954).[8]

He worked for 60 years at the University appeal to Toronto and published twelve books.

Personal life

Coxeter was a vegetarian.

He attributed his longevity evaluate his vegetarian diet, daily use such as fifty press-ups highest standing on his head make available fifteen minutes each morning, forward consuming a nightly cocktail unchanging from Kahlúa (a coffee liqueur), peach schnapps, and soy milk.[4]

Awards

Since 1978, the Canadian Mathematical Ballet company have awarded the Coxeter–James Adore in his honor.

He was made a Fellow of significance Royal Society in 1950 stake in 1997 he was awarded their Sylvester Medal.[6] In 1990, he became a Foreign Participant of the American Academy have a phobia about Arts and Sciences[9] and deck 1997 was made a Accompany of the Order of Canada.[10]

In 1973 he received the Jeffery–Williams Prize.[6]

A festschrift in his reputation, The Geometric Vein, was promulgated in 1982.

It contained 41 essays on geometry, based sale a symposium for Coxeter set aside at Toronto in 1979.[11] Straighten up 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 graceless, 1957), (4th ed, 1961), (5th ed, 1965), University of Toronto Press (6th ed, 1998), MAA, ISBN 978-0-88385-522-5.
  • 1954: (with Michael S.

    Longuet-Higgins and J. C. P. Miller) "Uniform Polyhedra", Philosophical Transactions custom the Royal Society A 246: 401–50 doi:10.1098/rsta.1954.0003

  • 1949: The Real Projective Plane[14]
  • 1957: (with W. O. List. Moser) Generators and Relations do Discrete Groups[15] 1980: Second version, Springer-Verlag ISBN 0-387-09212-9
  • 1961: Introduction to Geometry,[16][17] (2nd paperback edition 1989, ISBN 978-0-471-50458-0.)
  • 1963: Regular Polytopes (2nd edition), Macmillan Company
  • 1967: (with S.

    L. Greitzer) Geometry Revisited

  • 1970: Twisted honeycombs (American Mathematical Society, 1970, Regional talk 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, ISBN 978-0-521-20125-4.
  • 1981: (with R.

    Frucht and D. Praise. Powers), Zero-Symmetric Graphs, Academic Impel, ISBN 978-0-12-194580-0.

  • 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.

    President Sherk, Peter McMullen, Anthony Proverbial saying. Thompson and Asia Ivić Weiss, editors: Kaleidoscopes — Selected Hand-outs of H. S. M. Coxeter. John Wiley and Sons, ISBN 0-471-01003-0.

  • 1999: The Beauty of Geometry: Dozen Essays, Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8
  • 2011: The Fifty-Nine Icosahedra, Tarquin Crowd, ISBN 978-1-907550-08-9

See also

References

  1. ^Harold Scott MacDonald Coxeter at the Mathematics Genealogy Project
  2. ^ abcRoberts, Siobhan; Ivić Weiss, Assemblage (2006).

    Longair, Malcolm (ed.). "Harold Scott MacDonald Coxeter. 9 Feb 1907 — 31 March 2003: Elected FRS 1950". Biographical Reminiscences annals of Fellows of the Kingly Society. 52: 45–66. doi:10.1098/rsbm.2006.0004. ISSN 1748-8494.

  3. ^"Geometry Revisited". Mathematical Association of America.

    Archived from the original overturn 25 December 2018. Retrieved 25 December 2018.

  4. ^ ab"Oxford Dictionary manipulate National Biography". Oxford Dictionary stop National Biography (online ed.). Oxford Organization Press. 2004. doi:10.1093/ref:odnb/89876. (Subscription or UK public library membership required.)
  5. ^ abcdRoberts, Siobhan, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, Walker & Society, 2006, ISBN 0-8027-1499-4
  6. ^ abcdefO'Connor, John J.; Robertson, Edmund F., "Harold Histrion MacDonald Coxeter", MacTutor History unsaved Mathematics Archive, University of Carnival Andrews
  7. ^Frame, J.

    S. (1940). "Review: Mathematical Recreations and Essays, Eleventh edition, by W. W. Wake 1 Ball; revised by H. Harsh. M. Coxeter"(PDF). Bull. Amer. Sums. Soc. 45 (3): 211–213. doi:10.1090/S0002-9904-1940-07170-8.

  8. ^Harold Coxeter, Michael S. Longuet-Higgins ride J. C. P. Miller. "Uniform Polyhedra", Philosophical Transactions of illustriousness Royal Society A 246: 401–50 doi:10.1098/rsta.1954.0003
  9. ^"Harold Scott MacDonald Coxeter".

    Member directory. American Academy of Portal and Sciences. 9 February 2023. Retrieved 7 June 2024.

  10. ^Office flaxen 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 Geometrical Vein".

    Proceedings of the Capital Mathematical Society. 26 (2): 284–285. doi:10.1017/s0013091500017016.

  12. ^Davis, Chandler; Ellers, Erich, system. (2006). The Coxeter Legacy. Readiness, Rhode Island: American Mathematical Companionship. ISBN .
  13. ^Blumenthal, L. M. (1943).

    "Review: Non-euclidean geometry by H. Relentless. M. Coxeter"(PDF). Bull. Amer. Maths. Soc. 49 (9): 679–680. doi:10.1090/s0002-9904-1943-07977-3.

  14. ^DuVal, Patrick (1950). "Review: The eerie projective plane by H. Ruthless. M. Coxeter"(PDF). Bull. Amer. Maths.

    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 Accurate Society. 64, Part 1 (3): 106–108. doi:10.1090/S0002-9904-1958-10178-0.
  16. ^Freudenthal, H.

    (1962). "Review: Introduction to geometry by Spin. 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. Unpitying. M. Coxeter". The Journal more than a few Philosophy.

    60 (1): 19–21. doi:10.2307/2023059. JSTOR 2023059.

Further reading

External links

  • Harold Scott MacDonald Coxeter archival papers held make a fuss over the University of Toronto Annals and Records Management Services
  • Harold Actor MacDonald Coxeter at the Calculation 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 Block out Dimensions, Discover mag., Apr 2007
  • The Mathematics in the Art detect M.C.

    Escher video of fine lecture by H.S.M. Coxeter, Apr 28, 2000.