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Coxeter on people and polytopes. (English) Zbl 1072.01020

Rowe describes some aspects of the legacy of H. S. M. Coxeter in the history of mathematics and points out that Coxeter enriched our historical understanding of how classical geometry helped inspire what has sometimes been called the nineteenth century’s non-Euclidean revolution. Rowe focuses on Coxeter’s work on polytopes and has a thorough look at Coxeter’s classical book “Regular Polytopes” published in 1948 which summarized a 24-year labour and contained a lot of historical remarks in a style that is typical of Coxeter. Following Coxeter’s description he especially appreciates L. Schläfli who introduced the now standard Schläfli symbol and who was the first to recognize that we get “Exotic polytopes” only in dimension three and four. Furtheron Rowe discusses the work of W. I. Stringham, his influence on modern art and gives an impression of Coxeter’s attitude to the intuitive approach to the fourth dimension. This leads directly to Coxeter’s friendship with Alicia Boole Stott as well as the relations and the genealogy of the Boole family. Rowe closes his fine and interesting portrayal of Coxeter and his world of polytopes with a look at Coxeter as promoter of geometrical art and his friendship to M. C. Escher.

MSC:

01A60 History of mathematics in the 20th century
01A55 History of mathematics in the 19th century
52-03 History of convex and discrete geometry

Biographic References:

Coxeter, H. S. M.
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References:

[1] Coxeter, H. S. M., Regular Polytopes (1973), New York: Dover, New York
[2] Coxeter, H. S. M., “The non-Euclidean symmetry of Escher’s Picture ‘Circle Limit III’,”, Leonardo, 12, 19-25 (1979) · doi:10.2307/1574078
[3] Coxeter, H. S. M., “Review of M. C. Escher: His Life and Complete Graphic Work,” Mathematical Intelligencer, 7, 1, 59-69 (1985)
[4] Coxeter, H. S. M., “The Trigonometry of Escher’s Woodcut ‘Circle Limit III’,”, Mathematical Intelligencer, 18, 4, 42-46 (1996) · Zbl 0861.01022 · doi:10.1007/BF03026752
[5] Douglas Dunham, “Hyperbolic Art and the Poster Pattern,” Math Awareness Month-April 2003, http://mathfoum.org/mam/03/essay1.html.
[6] Henderson, Linda Dalrymple, The Fourth Dimension and Non-Euclidean Geometry in Modern Art (1983), Princeton: Princeton University Press, Princeton · Zbl 1270.00036
[7] Hilbert, David; Cohn-Vossen, Stephen, Anschauliche Geometrie (1932), Berlin: Springer, Berlin · Zbl 0005.11202 · doi:10.1007/978-3-662-36685-1
[8] Hinton, Charles Howard; Rucker, Rudolph, Speculations on the Fourth Dimension: Selected Writings of C. H. Hinton (1980), New York: Dover, New York
[9] Manning, Henry Parker, Geometry of Four Dimensions (1914), New York: Dover, New York · Zbl 0070.15904
[10] Manning, Henry Parker, The Fourth Dimension Simply Explained (1921), New York: Scientific American Publishing, New York · JFM 48.0646.12
[11] Michalowicz, Karen Dee; Calinger, Ronald, “Mary Everest Boole (1832-1916): An Erstwhile Pedagogist for Contemporary Times,”, Vita Mathematica: Historical Research and Integration with Teaching (1996), Washington, D.C.: Mathematical Association of America, Washington, D.C.
[12] Ivars Peterson, “Algebra Philosophy, and Fun,” www.ma.org/mathland/mathtrek_1_17_00.html. · Zbl 0997.00524
[13] Schläfli, Ludwig, “Theorie der vielfachen Kontinuität,”, Denkschriften der Schweizerischen naturforschenden Gesell-schaft, 38, 1-237 (1901) · JFM 32.0083.10
[14] Sommerville, Duncan M. Y., An Introduction to Geometry of N Dimensions (1929), New York: Dover, New York · JFM 55.0953.01
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