Polygonal numbers are a type of figurate number that can be arranged in the shape of a polygon. They are defined by the number of sides of the polygon. For example, triangular numbers represent points that can form an equilateral triangle, while square numbers can be arranged into a square shape. Each polygonal number can be calculated using a specific formula based on the number of sides. The general formula for the n-th k-gonal number is given by P(k, n) = \fracn((k-2)n - (k-4))2 . Here, k represents the number of sides, and n is the position in the sequence. This allows for the generation of various types of polygonal numbers, such as pentagonal and hexagonal numbers.