Norman Johnson (mathematician)

Summary

Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician at Wheaton College, Norton, Massachusetts.[1]

Norman Johnson
Born(1930-11-12)November 12, 1930
Chicago, United States
DiedJuly 13, 2017(2017-07-13) (aged 86)
Alma materUniversity of Toronto
Known forJohnson solid (1966)
Scientific career
FieldsMathematics
InstitutionsWheaton College, Norton, Massachusetts
Doctoral advisorH. S. M. Coxeter

Early life and education

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Norman Johnson was born on November 12, 1930 in Chicago. His father had a bookstore and published a local newspaper.[1]

Johnson earned his undergraduate mathematics degree in 1953 at Carleton College in Northfield, Minnesota[2] followed by a master's degree from the University of Pittsburgh.[1] After graduating in 1953, Johnson did alternative civilian service as a conscientious objector.[1] He earned his PhD from the University of Toronto in 1966 with a dissertation title of The Theory of Uniform Polytopes and Honeycombs under the supervision of H. S. M. Coxeter. From there, he accepted a position in the Mathematics Department of Wheaton College in Massachusetts and taught until his retirement in 1998.[1]

Career

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In 1966, he enumerated 92 convex non-uniform polyhedra with regular faces. Victor Zalgaller later proved (1969) that Johnson's list was complete, and the set is now known as the Johnson solids.[3][4]

Johnson is also credited with naming all the uniform star polyhedra and their duals, as published in Magnus Wenninger's model building books: Polyhedron models (1971) and Dual models (1983).[5]

Death and final works

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He completed final edits for his book Geometries and Transformations just before his death on July 13, 2017, and nearly completed his manuscript on uniform polytopes.[1]

Works

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  • ———— (1960-05-01). "A Geometric Model for the Generalized Symmetric Group". Canadian Mathematical Bulletin. 3 (2): 133–142. doi:10.4153/CMB-1960-016-7. S2CID 124822323.
  • Grünbaum, Branko; ———— (January 1965). "The Faces of a Regular-Faced Polyhedron". Journal of the London Mathematical Society. s1-40 (1): 577–586. doi:10.1112/jlms/s1-40.1.577.
  • ———— (January 1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. ISSN 0008-414X. MR 0185507. S2CID 122006114. Zbl 0132.14603.
  • ———— (1966). The theory of uniform polytopes and honeycombs (PhD thesis). University of Toronto. OL 14849556M. Archived from the original on 2022-05-20. Retrieved 2022-05-20.
  • ———— (December 1969). "Euclidean Geometry and Convexity by Russell V. Benson (review)". The American Mathematical Monthly. 76 (10): 1165–1160. doi:10.2307/2317227. JSTOR 2317227.
  • ———— (January 1981). "Absolute Polarities and Central Inversions". In Davis, C.; Grünbaum, B.; Sherk, F. A. (eds.). The Geometric Vein. New York City: Springer Nature. pp. 443–464. doi:10.1007/978-1-4612-5648-9_28. ISBN 978-1-4612-5648-9.
  • ————; Weiss, Asia Ivić (July 1999). "Quaternionic modular groups". Linear Algebra and Its Applications. 295 (1): 159–189. doi:10.1016/S0024-3795(99)00107-X.
  • ————; Weiss, Asia Ivić (December 1999). "Quadratic Integers and Coxeter Groups". Canadian Journal of Mathematics. 51 (6): 1307–1336. doi:10.4153/CJM-1999-060-6. S2CID 111383205.
  • ————; Kellerhals, Ruth; Ratcliffe, John G.; Tschantz, Steven T. (December 1999). "The size of a hyperbolic Coxeter simplex". Transformation Groups. 4 (4): 329–353. doi:10.1007/BF01238563. S2CID 123105209.
  • ————; Kellerhals, Ruth; Ratcliffe, John G.; Tschantz, Steven T. (2002-04-15). "Commensurability classes of hyperbolic Coxeter groups". Linear Algebra and Its Applications. 345 (1–3): 119–147. doi:10.1016/S0024-3795(01)00477-3.
  • ———— (2012). "Regular Inversive Polytopes". In Deza, Michel; Petitjean, Michel; Markov, Krassimir (eds.). Mathematics of Distances and Applications. Sofia: ITHEA. Archived from the original on 2022-05-20. Retrieved 2022-05-19.
  • ———— (2018-06-07). Geometries and Transformations. ISBN 978-1-107-10340-5. OCLC 1043026091. OL 27839953M. Retrieved 2022-05-20.

References

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  1. ^ a b c d e f Weiss, Asia Ivić; Stehle, Eva Marie (2017). "Norman W. Johnson (12 November 1930 to 13 July 2017)". The Art of Discrete and Applied Mathematics. 1: #N1.01. doi:10.26493/2590-9770.1231.403. ISSN 2590-9770. Archived from the original on 2022-05-19. Retrieved 2022-05-19.
  2. ^ "Norman Johnson '53". Carleton College. 2017-07-18. Archived from the original on 2022-05-19. Retrieved 2022-05-19.
  3. ^ Hart, George W. "Johnson solids". George W. Hart. Archived from the original on 2021-08-30. Retrieved 2016-06-10.
  4. ^ Weisstein, Eric W. "Johnson Solid". MathWorld. Retrieved 2016-06-10.
  5. ^ Wenninger, Magnus (1983). Dual Models. Cambridge University Press. p. xii. doi:10.1017/CBO9780511569371. ISBN 978-0-521-54325-5. MR 0730208.
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