About Math Contest Convex K Edge Shape Counting Problem Research

This paper is going to study combinatorial geometry enumeration of mathematical competitions based on combinatorial enumeration, particular in how to calculate the number of convex polygons.At the beginning of the paper we make a brief introduction to some related fundamental knowledge of combinatorial geometry and enumeration methods, then the existing conditions of some special convex polygons are studied on the basis of something related to mathematical competition and discuss the enumeration of convex k-gons containing in regular polygons and general convex polygons, furthermore, the enumeration of triangles and parallelograms are considered in the triangular web-array and dot-array, finally we make some summations and remarks.According to analyzing the references, we discusses in competition mathematics the applications of the enumeration of convex polygons in combinatorial geometry and the designs of such kinds of questions aiming at grasping the laws of setting questions in mathematical competitions.The innovations of the paper are to show some propositions and corollaries and giving some simple solutions and generalizations to some questions in mathematical competitions independently.