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Cutting a polygon into triangles of equal fnareas. (English) Zbl 1186.52015
MSC:
52C20Tilings in 2 dimensions (discrete geometry)
52B45Dissections and valuations
References:
[1]E. A. Kasimatis, Dissections of regular polygons into triangles of equal areas,Discrete and Comp. Geometry 4 (1989), 375–381. · Zbl 0675.52005 · doi:10.1007/BF02187738
[2], and S. Stein, Equidissections of polygons,Discrete Math. 85 (1990), 281–294 · Zbl 0736.05028 · doi:10.1016/0012-365X(90)90384-T
[3]D. G. Mead, Dissection of hypercubes into simplices,Proc. Amer. Math. Soc. 76 (1979), 302–304. · doi:10.1090/S0002-9939-1979-0537093-6
[4]P. Monsky, On dividing a square into triangles,Amer. Math. Monthly 77 (1970), 161–164. · Zbl 0187.19701 · doi:10.2307/2317329
[5]—-, A conjecture of Stein on plane dissections,Math. Zeit. 205 (1990), 583–592. · Zbl 0693.51008 · doi:10.1007/BF02571264
[6]I. Praton, Cutting Polyominos into Equal-Area Triangles,Amer. Math. Monthly 109 (2002) 818–826. · Zbl 1026.05027 · doi:10.2307/3072370
[7]F. Richman and J. Thomas, Problem 5471,Amer. Math. Monthly 74 (1967), 329. · doi:10.2307/2316056
[8]S. Stein, Equidissections of centrally symmetric octagons,Aequationes Math. 37 (1989), 313–318. · Zbl 0681.52008 · doi:10.1007/BF01836454
[9]S. Stein and S. Szabo, Algebra and Tiling,Mathematical Association of America, Washington, D. C. 1994.
[10]—- Cutting a polyomino into triangles of equal areas,Amer. Math. Monthly 106 (1999), 255–257. · doi:10.2307/2589681
[11]—- A generalized conjecture abourt cutting a polygon into triangles of equal areas,Discrete and Comp. Geometry 24 (2000), 141–145
[12]J. Thomas, A dissection problem,Math. Mag. 41 (1968), 187–190. · Zbl 0164.51502 · doi:10.2307/2689143