Equilateral triangles, squares, and pentagons are all examples of regular polygons. All polygons have at least three sides. In a polygon, the point at which two sides intersect is called a vertex. So a pentagon has five vertices (the plural of vertex). Two vertices are contiguous if they are connected by one of the sides of the polygon. The polygon of this problem has a positive real number associated with each vertex. All of these real numbers are different. At each vertex, the real number associated with it is the product of the two real numbers associated with the two contiguous vertices. How many sides does our polygon have? Prove that your answer is the only possible one to the question.