Harold Scott MacDonald Coxeter | |
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| Born | (1907-02-09)9 February 1907 London, England |
| Died | 31 March 2003(2003-03-31) (aged 96) Toronto, Ontario, Canada |
| Alma mater | University of Cambridge (B.A., 1929; Ph.D., 1931) |
| Known for | Coxeter 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 |
| Children | a daughter, Susan Thomas, and a son, Edgar |
| Awards |
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| Scientific career | |
| Fields | Geometry |
| Institutions | University of Toronto |
| Doctoral advisor | H. F. Baker[1] |
| Doctoral students | |
Harold Scott MacDonald "Donald"Coxeter ([ˈkoksɛtɛr],[ˈkɒksətər])CC FRS FRSC (9 February 1907 – 31 March 2003)[2] was a British-Canadiangeometer and mathematician. He is regarded as one of the greatest geometers of the 20th century.[3]
Coxeter was born in England and educated at theUniversity of Cambridge, with student visits toPrinceton University. He worked for 60 years at theUniversity of Toronto in Canada, from 1936 until his retirement in 1996, becoming a full professor there in 1948. His many honours included membership in theRoyal Society of Canada, theRoyal Society, and theOrder of Canada.
He was an author of 12 books, includingThe Fifty-Nine Icosahedra (1938) andRegular Polytopes (1947). Many concepts in geometry andgroup theory are named after him, including theCoxeter graph,Coxeter groups,Coxeter's loxodromic sequence of tangent circles,Coxeter–Dynkin diagrams, and theTodd–Coxeter algorithm.
Coxeter was born inKensington, 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 withnitrous 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 theRoyal Academy of Arts. A maternal cousin was the architect SirGiles Gilbert Scott.[4][2]
In his youth, Coxeter composed music and was an accomplished pianist at the age of 10.[5] He felt thatmathematics and music were intimately related, outlining his ideas in a 1962 article on "Music and Mathematics" in theCanadian Music Journal.[5]
He was educated atKing Alfred School, London, andSt George's School, Harpenden, where his best friend was John Flinders Petrie, later a mathematician for whomPetrie polygons were named. He was accepted atKing's College, Cambridge, in 1925, but decided to spend a year studying in hopes of gaining admittance toTrinity 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 (asSenior Wrangler) in 1928, and his doctorate in 1931.[5][6] In 1932 he went toPrinceton University for a year as aRockefeller Fellow, where he worked withHermann Weyl,Oswald Veblen, andSolomon Lefschetz.[6] Returning to Trinity for a year, he attendedLudwig Wittgenstein's seminars on thephilosophy of mathematics.[5] Wittgenstein selected Coxeter and others to take notes of his lectures, the collection of which later becameThe Blue Book.[7] 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 andP. Du Val, H. T. Flather, andJohn Flinders Petrie publishedThe Fifty-Nine Icosahedra withUniversity of Toronto Press. In 1940 Coxeter edited the eleventh edition ofMathematical Recreations and Essays,[8] originally published byW. W. Rouse Ball in 1892. He was elevated toprofessor in 1948. He was elected a Fellow of theRoyal Society of Canada in 1948 and aFellow of the Royal Society in 1950. He metM. C. Escher in 1954 and the two became lifelong friends; his work on geometric figures helped inspire some of Escher's works, particularly theCircle Limit series based onhyperbolictessellations. He also inspired some of the innovations ofBuckminster Fuller.[6] Coxeter,M. S. Longuet-Higgins andJ. C. P. Miller were the first to publish the fulllist of uniform polyhedra (1954).[9]
He worked for 60 years at theUniversity of Toronto and published twelve books.
Coxeter was avegetarian. 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 fromKahlúa (a coffee liqueur),peach schnapps, andsoy milk.[4]
Since 1978, theCanadian Mathematical Society have awarded theCoxeter–James Prize in his honor.
He was made aFellow of the Royal Society in 1950 and in 1997 he was awarded theirSylvester Medal.[6] In 1990, he became a Foreign Member of theAmerican Academy of Arts and Sciences[10] and in 1997 was made aCompanion of theOrder of Canada.[11]
In 1973 he received theJeffery–Williams Prize.[6]
Afestschrift 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.[12] A second such volume,The Coxeter Legacy, was published in 2006 based on a Toronto Coxeter symposium held in 2004.[13]
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