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polygonal number





The number of equally spaced dots needed to draw a polygon. Polygonal numbers, which are a type of figurate number, include square numbers, triangular numbers, pentagonal numbers, and hexagonal numbers.

Polygonal numbers form an arithmetic sequence of the second order. The general term of these sequences is
zn = n/2 [2 + (n - 1)d],
where d is one of the numbers 1, 2, 3, ...

With d = 1 we obtain the triangular numbers: 1, 3, 6, 10, 15, ...
With d = 2 we obtain the square numbers: 1, 4, 9, 16, 25, ...
With d = 3 we obtain the pentagonal numbers: 1, 5, 12, 22, 35, ...


Related category

   • TYPES OF NUMBERS