Reflection groups and the pizza theorem
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Yu. A. Brailov
Translated by: the author - St. Petersburg Math. J. 33 (2022), 891-896
- DOI: https://doi.org/10.1090/spmj/1732
- Published electronically: October 31, 2022
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Abstract:
The classical theorem about cutting a round pizza into 8 pieces with straight cuts passing through an arbitrary internal point and forming angles of 45 degrees says that the total areas of odd and even pieces are equal if those pieces are ordered around the center of cutting. The current paper proposes a generalization of the Pizza theorem to any dimension and discovers a relationship with the finite reflection group of the series $B_n$.References
- Charles R. Wall, Charles W. Trigg, Gerald C. Dodds, Huseyin Demir, Leon Bankoff, John Beidler, Murray S. Klamkin, Sidney Kravitz, Zalman Usiskin, C. Stanley Ogilvy, Kaidy Tan, Stanley Rabinowitz, C. J. Mozzochi, L. J. Upton, Michael Goldberg, J. Aczel, M. B. McNeil, Kenneth A. Ribet, S. Spital, Albert Wilansky, Bart Park, and John H. Tiner, Problems and Solutions, Math. Mag. 41 (1968), no. 1, 42. MR 1571739, DOI 10.2307/2687962
- Rick Mabry and Paul Deiermann, Of cheese and crust: a proof of the pizza conjecture and other tasty results, Amer. Math. Monthly 116 (2009), no. 5, 423–438. MR 2510839, DOI 10.4169/193009709X470317
- Larry Carter and Stan Wagon, Proof without Words: Fair Allocation of a Pizza, Math. Mag. 67 (1994), no. 4, 267. MR 1573034, DOI 10.1080/0025570X.1994.11996228
- A. L. Onishchik and È. B. Vinberg, Lie groups and algebraic groups, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1990. Translated from the Russian and with a preface by D. A. Leites. MR 1064110, DOI 10.1007/978-3-642-74334-4
- N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
Bibliographic Information
- Yu. A. Brailov
- Affiliation: M. V. Lomonosov Moscow State University, Vorobyevy gory 119992, Moscow, Russia
- Email: yury.brailov@gmail.com
- Received by editor(s): July 19, 2020
- Published electronically: October 31, 2022
- © Copyright 2022 American Mathematical Society
- Journal: St. Petersburg Math. J. 33 (2022), 891-896
- MSC (2020): Primary 51F15
- DOI: https://doi.org/10.1090/spmj/1732