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Cutting a polygon into triangles of equal fnareas. (English) Zbl 1186.52015

52C20Tilings in $2$ dimensions (discrete geometry)
52B45Dissections and valuations
Full Text: DOI
[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. · Zbl 0423.51012 · 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 · Zbl 0968.52011
[12] J. Thomas, A dissection problem,Math. Mag. 41 (1968), 187--190. · Zbl 0164.51502 · doi:10.2307/2689143