Norman Johnson (mathematician)
Norman Johnson | |
|---|---|
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| Born | November 12, 1930 Chicago, United States |
| Died | July 13, 2017 (aged 86) |
| Alma mater | University of Toronto |
| Known for | Johnson solid (1966) |
| Scientific career | |
| Fields | Mathematics |
| Workplaces | Wheaton College, Norton, Massachusetts |
| H. S. M. Coxeter | |
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was an American mathematician at Wheaton College, Norton, Massachusetts.[1]
Early life and education
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.[T66] From there, he accepted a position in the Mathematics Department of Wheaton College in Massachusetts and taught until his retirement in 1998.[1]
Career
In 1966, Johnson published a paper titled Convex Polyhedra with Regular Faces.[A66] Inside, it contained the list of 92 convex polyhedra with regular faces,[1] along with the coined prefixes on naming some solids; encompassing the family of prisms, antiprisms, and other uniform polyhedra brings up 112 solids in total.[3] Victor Zalgaller later proved in 1969 that Johnson's list of 92 solids was complete, and the set is now known as the Johnson solids or Johnson–Zalgaller solid.[4][3][5]
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).[6]
Death and final works
He completed final edits for his book Geometries and Transformations[B18] just before his death on July 13, 2017, and nearly completed his manuscript on uniform polytopes.[1]
Works
Thesis
| T66. | ———— (1966). The theory of uniform polytopes and honeycombs (PhD thesis). University of Toronto. OL 14849556M. Retrieved 2022-05-20. {{cite thesis}}: CS1 maint: deprecated archival service (link) ONLINE |
Articles and books
| A60. | ———— (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. |
| A65. | 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. |
| A66. | ———— (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. |
| A69. | ———— (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. |
| A81. | ———— (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. |
| A99a. | ————; 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. |
| A99b. | ————; 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. |
| A99c. | ————; 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. |
| A02. | ————; 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. |
| A12. | ———— (2012). "Regular Inversive Polytopes". In Deza, Michel; Petitjean, Michel; Markov, Krassimir (eds.). Mathematics of Distances and Applications. Sofia: ITHEA. Retrieved 2022-05-19. {{cite conference}}: CS1 maint: deprecated archival service (link) |
| B18. | ———— (2018-06-07). Geometries and Transformations. Cambridge University Press. ISBN 978-1-107-10340-5. OCLC 1043026091. OL 27839953M. Retrieved 2022-05-20. |
References
- 1 2 3 4 5 6 7 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. Retrieved 2022-05-19.
{{cite journal}}: CS1 maint: deprecated archival service (link) - ↑ "Norman Johnson '53". Carleton College. 2017-07-18. Retrieved 2022-05-19.
{{cite web}}: CS1 maint: deprecated archival service (link) - 1 2 Berman, M. (1971). "Regular-faced convex polyhedra". Journal of the Franklin Institute. 291 (5): 329–352. Bibcode:1971FrInJ.291..329B. doi:10.1016/0016-0032(71)90071-8. MR 0290245.
- ↑ Zalgaller, V. A. (1969). Convex Polyhedra with Regular Faces. Springer. ISBN 978-1-489-95671-2.
- ↑ Araki, Yoshiaki; Horiyama, Takashi; Uehara, Ryuhei (2015). "Common Unfolding of Regular Tetrahedron and Johnson-Zalgaller Solid". In Rahman, M. Sohel; Tomita, Etsuji (eds.). WALCOM: Algorithms and Computation. Lecture Notes in Computer Science. Vol. 8973. Cham: Springer International Publishing. pp. 294–305. doi:10.1007/978-3-319-15612-5_26. ISBN 978-3-319-15612-5.
- ↑ Wenninger, Magnus (1983). Dual Models. Cambridge University Press. p. xii. doi:10.1017/CBO9780511569371. ISBN 978-0-521-54325-5. MR 0730208.
External links
- Norman W. Johnson at the Mathematics Genealogy Project
- Norman W. Johnson Endowed Fund in Mathematics and Computer Science Archived 2017-06-16 at the Wayback Machine at Wheaton College