Dissection of the hypercube into simplexes
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- by D. G. Mead PDF
- Proc. Amer. Math. Soc. 76 (1979), 302-304 Request permission
Abstract:
A generalization of Sperner’s Lemma is proved and, using extensions of p-adic valuations to the real numbers, it is shown that the unit hypercube in n dimensions can be divided into m simplexes all of equal hypervolume if and only if m is a multiple of n!. This extends the corresponding result for $n = 2$ of Paul Monsky.References
- George Bachman, Introduction to $p$-adic numbers and valuation theory, Academic Press, New York-London, 1964. MR 0169847
- Paul Monsky, On dividing a square into triangles, Amer. Math. Monthly 77 (1970), 161–164. MR 252233, DOI 10.2307/2317329
- John Thomas, A dissection problem, Math. Mag. 41 (1968), 187–191. MR 236805, DOI 10.2307/2689143
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 302-304
- MSC: Primary 52A25
- DOI: https://doi.org/10.1090/S0002-9939-1979-0537093-6
- MathSciNet review: 537093