Figurate Number

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

Name	Formula
Biquadratic Number
Centered Cube Number
Centered Pentagonal Number
Centered Square Number
Centered Triangular Number
Cubic Number
Decagonal Number
Gnomic Number
Heptagonal Number
Hex Number
Heptagonal Pyramidal Number
Hexagonal Number
Hexagonal Pyramidal Number
Octagonal Number
Octahedral Number
Pentagonal Number
Pentagonal Pyramidal Number
Pentatope Number
Pronic Number
Rhombic Dodecahedral Number
Square Number
Stella Octangula Number
Tetrahedral Number
Triangular Number
Truncated Octahedral Number
Truncated Tetrahedral Number

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.

• Trace (Complex)
• Trace (Group)
• Trace (Map)
• Trace (Matrix)
• Trace (Tensor)
• Tractory
• Tractrix
• Tractrix Evolute
• Tractrix Radial Curve
• Tractroid
• Transcendental Curve
• Transcendental Equation
• Transcendental Function
• Transcendental Number
• Transcritical Bifurcation
• Transfer Function
• Convergent Sequence
• Convergent Series
• Conversion Period
• Convex
• Convex Function
• Convex Hull
• Convex Optimization Theory
• Convex Polygon
• Convex Polyhedron