Norman Johnson (mathematician)

Norman Johnson was born on {{date2|November|12, |1930}} in Chicago. His father had a bookstore and published a local newspaper.{{r|Weiss}}

Johnson earned his undergraduate mathematics degree in 1953 at Carleton College in Northfield, Minnesota{{refn|{{Cite web |date=July 18, 2017 |title=Norman Johnson '53 |url=https://www.carleton.edu/alumni/farewells/news/norman-johnson-53/ |url-status=live |archive-url=https://archive.today/20220519234859/https://www.carleton.edu/alumni/farewells/news/norman-johnson-53/ |archive-date=May 19, 2022 |access-date=May 19, 2022 |website=Carleton College |language=en-US}}}} followed by a master's degree from the University of Pittsburgh.{{r|Weiss}} After graduating in 1953, Johnson did alternative civilian service as a conscientious objector.{{r|Weiss}} 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.{{r|Weiss}}

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.{{refn|{{Cite web |last=Hart |first=George W. |author-link=George W. Hart |title=Johnson solids |url=http://www.georgehart.com/virtual-polyhedra/johnson-info.html |url-status=live |archive-url=https://archive.today/20210830094735/http://www.georgehart.com/virtual-polyhedra/johnson-info.html |archive-date=August 30, 2021 |access-date=June 10, 2016 |language=en-US |website=George W. Hart}}}}{{refn|{{MathWorld|id=JohnsonSolid|title=Johnson Solid|access-date=June 10, 2016}}}}

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).{{refn|{{Cite book |last=Wenninger |first=Magnus |title=Dual Models |publisher=Cambridge University Press |year=1983 |isbn=978-0-521-54325-5 |page=xii |doi=10.1017/CBO9780511569371 |mr=730208 |author-link=Magnus Wenninger}}}}

He completed final edits for his book Geometries and Transformations just before his death on {{date2|July|13, |2017}}, and nearly completed his manuscript on uniform polytopes.{{r|Weiss}}

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• {{Cite journal |last=Johnson |first=Norman W. |author-mask=4 |date=May 1, 1960 |title=A Geometric Model for the Generalized Symmetric Group |journal=Canadian Mathematical Bulletin |volume=3 |issue=2 |pages=133–142 |doi=10.4153/CMB-1960-016-7|s2cid=124822323 |doi-access=free }}
• {{Cite journal |last1=Grünbaum |first1=Branko |author-link=Branko Grünbaum |last2=Johnson |first2=Norman W. |date=January 1965 |title=The Faces of a Regular-Faced Polyhedron |journal=Journal of the London Mathematical Society |volume=s1-40 |issue=1 |pages=577–586 |doi=10.1112/jlms/s1-40.1.577 |author-mask2=4}}
• {{Cite journal |last=Johnson |first=Norman W. |author-mask=4 |date=January 1966 |title=Convex polyhedra with regular faces |journal=Canadian Journal of Mathematics |volume=18 |pages=169–200 |doi=10.4153/cjm-1966-021-8 |issn=0008-414X |mr=0185507 |zbl=0132.14603 |s2cid=122006114|doi-access=free }}
• {{Cite thesis |last=Johnson |first=Norman W |title=The theory of uniform polytopes and honeycombs |date=1966 |degree=PhD |publisher=University of Toronto |url=https://www.tib.eu/en/search/id/TIBKAT:22693604X/ |author-mask=4 |archive-url=https://archive.today/20220520024719/https://www.tib.eu/en/search/id/TIBKAT:22693604X/ |archive-date=May 20, 2022 |access-date=May 20, 2022 |ol=14849556M}} [http://roice3.org/ruen/tup ONLINE]
• {{Cite journal |last=Johnson |first=Norman W. |author-mask=4 |date=December 1969 |title=Euclidean Geometry and Convexity by Russell V. Benson (review) |journal=The American Mathematical Monthly |volume=76 |issue=10 |pages=1165–1160 |doi=10.2307/2317227 |jstor=2317227}}
• {{Cite conference |last=Johnson |first=Norman W. |author-mask=4 |date=January 1981 |title=Absolute Polarities and Central Inversions |location=New York City |publisher=Springer Nature |pages=443–464 |doi=10.1007/978-1-4612-5648-9_28 |isbn=978-1-4612-5648-9 |book-title=The Geometric Vein |editor1-last=Davis |editor1-first=C. |editor2-last=Grünbaum |editor2-first=B. |editor-link2=Branko Grünbaum |editor3-last=Sherk |editor3-first=F. A.}}
• {{Cite journal |last1=Johnson |first1=Norman W. |last2=Weiss |first2=Asia Ivić |author-mask=4 |date=July 1999 |title=Quaternionic modular groups |journal=Linear Algebra and Its Applications |volume=295 |issue=1 |pages=159–189 |doi=10.1016/S0024-3795(99)00107-X|doi-access=free }}
• {{Cite journal |last1=Johnson |first1=Norman W. |last2=Weiss |first2=Asia Ivić |author-mask=4 |date=December 1999 |title=Quadratic Integers and Coxeter Groups |journal=Canadian Journal of Mathematics |volume=51 |issue=6 |pages=1307–1336 |doi=10.4153/CJM-1999-060-6|s2cid=111383205 |doi-access=free }}
• {{Cite journal |last1=Johnson |first1=Norman W. |last2=Kellerhals |first2=Ruth |author-link2=Ruth Kellerhals |last3=Ratcliffe |first3=John G. |last4=Tschantz |first4=Steven T. |author-mask=4 |date=December 1999 |title=The size of a hyperbolic Coxeter simplex |journal=Transformation Groups |volume=4 |issue=4 |pages=329–353 |doi=10.1007/BF01238563|s2cid=123105209 }}
• {{Cite journal |last1=Johnson |first1=Norman W. |last2=Kellerhals |first2=Ruth |author-link2=Ruth Kellerhals |last3=Ratcliffe |first3=John G. |last4=Tschantz |first4=Steven T. |author-mask=4 |date=April 15, 2002 |title=Commensurability classes of hyperbolic Coxeter groups |journal=Linear Algebra and Its Applications |volume=345 |issue=1–3 |pages=119–147 |doi=10.1016/S0024-3795(01)00477-3|doi-access=free }}
• {{Cite conference |last=Johnson |first=Norman W. |author-mask=4 |date=2012 |title=Regular Inversive Polytopes |url=https://www.researchgate.net/publication/279194347 |publisher=ITHEA |archive-url=https://archive.today/20220520033305/https://www.researchgate.net/publication/279194347_Regular_Inversive_Polytopes |archive-date=May 20, 2022 |access-date=May 19, 2022 |book-title=Mathematics of Distances and Applications |editor1-last=Deza |editor1-first=Michel |editor2-last=Petitjean |editor2-first=Michel |editor3-last=Markov |editor3-first=Krassimir |place=Sofia |url-status=live}}
• {{Cite book |last=Johnson |first=Norman W. |url={{GBurl|id=adBVDwAAQBAJ}} |title=Geometries and Transformations |date=June 7, 2018 |publisher=Cambridge University Press |isbn=978-1-107-10340-5 |oclc=1043026091 |ol=27839953M |author-mask=4 |access-date=May 20, 2022}}

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{{Reflist}}

• {{MathGenealogy |id=16046|name=Norman W. Johnson}}
• [http://wheatoncollege.edu/mathematics/norman-johnson-fund/ Norman W. Johnson Endowed Fund in Mathematics and Computer Science] at Wheaton College

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{{DEFAULTSORT:Johnson, Norman}}

Category:1930 births

Category:2017 deaths

Category:20th-century American mathematicians

Category:University of Toronto alumni

Category:Wheaton College (Massachusetts) faculty