Polygonal numbers are a type of figurate number that can be arranged in the shape of a polygon. They are defined by a formula that relates to the number of sides of the polygon. For example, triangular numbers are formed by arranging dots in the shape of an equilateral triangle, while square numbers are arranged in a square shape. The general formula for the n-th k-gonal number is given by P(k, n) = \fracn((k-2)n - (k-4))2 , where k is the number of sides and n is the term number. This means that for any polygon, you can calculate how many dots would form that shape as you increase the number of layers.