FINDING INTEGRATED POLYGONS.docx

This paper proposes and proves a formula for calculating the maximum number of integrated polygons of a given type that can be formed within a larger polygon in a single combination without overlapping. The formula is expressed as Θ(α,n)=⌊α−2/n−2⌋, where n is the number of sides of the initial polygon, and α is the number of sides of the integrated polygon. The formula is derived from the properties of diagonal partitioning in polygons and provides a general approach for solving such problems. Examples are provided to illustrate the practical application of the formula.