Subdivision of a Regular Polygon

Abstract

The basic principle and techniques discussed in this research belongs to combinatorial analysis. Motivated by the problem in the international mathematics Olympiad of which, as written in, Lin Ziwei, a participant in the international mathematics Olympiad, age 14 then, was able to solve the problem of subdivision of a triangle into parallelogram with an hour. The researcher feels it is challenging to extend a concept of nth subdivision of triangle into subdivision of a regular polygon. In this research, results obtained include the explicit formula for giving the number of triangles in nth subdivision of any regular polygon and several illustrations leading into a conjecture on the non-existence of restricted polygons in the nth subdivision.