摘要
本文证明了二染色平面必定存在斜边长为ａ（ａ＞０），一个锐角为的单色顶点的直角三角形；必定存在内角为、且这两个角夹边为ａ的单色顶点三角形；必定存在边长为ａ、，的单色顶点的等腰三角形；必定存在位似比为ｋ的两个位似的凸多边形，并且每个多边形的顶点单色．
In this paper, the following conclusions on the two-colour-dyed plane are obtained. Onthe two-colour-dyed plane, for any given positive number a,there exists a right triangle withsingle-colour vertexes,the length of the hypotenuse of which is a and one of the acute anglesof which is π/6; there exists a triangle with single-colour vertexes,two internal angles ofwhich are 2π/7, 4π/7 and the4ength of the side between them is a;there exists an isoscelestriangle with single-colour vertexes, the lengths of the sides of which are a,respectively, and there are two homothetic convex polygons with homothetic ratio a,each ofthem having single-colour vertexes.
出处
《首都师范大学学报（自然科学版）》
1996年第3期104-108,共5页
Journal of Capital Normal University：Natural Science Edition
