A number which can be represented by a regular geometrical arrangement of equally spaced points. If the arrangement forms a Regular Polygon, the number is called a Polygonal Number. The polygonal numbers illustrated above are called triangular, square, pentagonal, and hexagon numbers, respectively. Figurate numbers can also form other shapes such as centered polygons, L-shapes, 3-dimensional solids, etc. The following table lists the most common types of figurate numbers.

**References**

Conway, J. H. and Guy, R. K. *The Book of Numbers.* New York: Springer-Verlag, pp. 30-62, 1996.

Dickson, L. E. ``Polygonal, Pyramidal, and Figurate Numbers.'' Ch. 1 in
*History of the Theory of Numbers, Vol. 2: Diophantine Analysis.* New York: Chelsea, pp. 1-39, 1952.

Goodwin, P. ``A Polyhedral Sequence of Two.'' *Math. Gaz.* **69**, 191-197, 1985.

Guy, R. K. ``Figurate Numbers.'' §D3 in *Unsolved Problems in Number Theory, 2nd ed.* New York:
Springer-Verlag, pp. 147-150, 1994.

Kraitchik, M. ``Figurate Numbers.'' §3.4 in *Mathematical Recreations.* New York: W. W. Norton, pp. 66-69, 1942.

© 1996-9

1999-05-26