polygonal number

Polygonal numbers are a type of figurate number that represent numbers as arrangements of dots forming geometric shapes, such as triangles or squares. These numbers were of particular interest to ancient Greek mathematicians, like the Pythagoreans, who believed numbers possessed specific characteristics and shapes.1

For example, triangular numbers, such as 1, 3, 6, and 10, are visualized as dots arranged in a triangle. Square numbers, like 1, 4, 9, and 16, are formed by arranging dots in a square array. Oblong numbers, such as 2, 6, 12, and 20, are represented by rectangular arrays where each row has one more dot than each column. These geometric representations have connections to algebraic expressions and are a part of number theory.12345