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关于一类特殊梯形的等面积三角形划分

On Cutting a Family of Special Trapezoids into Triangles of Equal Areas
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摘要 1970年 Monsky证明了正方形不能划分为奇数个面积相等的三角形 .Stein等人对梯形的等面积三角形划分作了深入的研究 ,得到了大量结果 .本文就未解决的问题作了进一步的讨论 ,即讨论一类特殊梯形的等面积三角形划分问题 . In 1970 P.Monsky proved that a square cannot be cut into an odd number of triangles of equal areas, recently S.Stein and many people have researched the problem about cutting trapezoids into triangles of equal areas, and obtained lots of results. In the present paper we discuss an unresolved problem about trapezoids, that is, on cutting trapezoids T(2 kn) into triangles of equal areas.
作者 苏战军
出处 《数学的实践与认识》 CSCD 北大核心 2004年第1期145-149,共5页 Mathematics in Practice and Theory
基金 河北省自然科学基金资助项目 ( 1 991 74)
关键词 梯形 等面积三角形划分 仿射变换 素数 同构映射 valuation complete dissection of equal areas trapezoid
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参考文献7

  • 1[1]Monsky P. On dividing a square into triangles[J]. Amer Math Monthly, 1970, (77): 163-164.
  • 2[2]Monsky P. A conjecture of Stein on plane dissection[J]. Math Z, 1990, (205): 583-592.
  • 3[3]Stein S. Equidissections of centrally octagons[J]. Aequations Math, 1989, (37): 113-118.
  • 4[4]Stein S. Cutting a polyomino into triangles of equal areas[J]. Amer Math Monthly, 1999, (106): 255-257.
  • 5[5]Stein S. A generalized conjecture about cutting a polygon into triangles of equal areas[J]. Discrete Comput Geom, 2000, (24): 141-145.
  • 6[6]Kasimatis E A. Dissections of regular polygons into triangles of equal areas[J]. Discrete and Computed Geometry, 1989, (4): 375-381.
  • 7[7]Stein S, SzabóS. Algebra and Tiling[M]. Washington DC, The Mathematical Association of America, 1994. 121-124.

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