摘要
1970年Monksy证明了正方形不能划分为奇数个面积相等的三角形 ,此性质已被推广到中心对称的多边形以及其它特殊的多边形 .本文证明 :对任意多边形K ,存在平面多边形簇 {Kn｜n∈N} 和 {K′n｜n ∈N} 使得{Kn｜n∈N}∪ {K′n｜n∈N} 中任何一个Kn 或K′n 都不能划分为奇数个面积相等的三角形并且limn→∞ Kn =K=limn→∞ K′n ,A(Kn) A(K) A(K′n) ,limn→∞ A(Kn) =A(K) =limn→∞ A(K′n) .
In 1970 Monsky proved that a square cannot be cut into an odd number of triangles of equal areas and this property was generalized to any centrally symmetric polygon and some other special polygons. In this paper we prove that for any ploygon K, there are two families of polygons {K n |n∈N} and {K′ n |n∈N} such that K n or K′ n (n∈N) cannot be cut into an odd number of triangles of equal areas and lim n→∞ K n =K= lim n → ∞ K′ n , A(K n ) A(K) A(K′ n ), lim n → ∞ A(K n )=A(K)= lim n → ∞ A(K′ n ).
出处
《河南师范大学学报（自然科学版）》
CAS
CSCD
2002年第4期95-97,共3页
Journal of Henan Normal University(Natural Science Edition)
基金
河北省自然科学基金资助项目 (编号 :199174 )
