Polygonal Number

In Mathematical, a polygonal number is a Nombre which can be represented by a regular Polygone. The Mathématicien S antiques discovered that numbers could be represented while arranging in a certain manner of stones or seeds. For example, number 10, can be represented by a Triangle

See also: triangular Number

But 10 cannot be represented by a Carré, whereas number 9, can be represented while having the crosses to form a square.

See also: square Number

Certain numbers, like 36, can be at the same time represented by a square and a triangle.

See also: triangular square Number

The method to increase a polygon consists in prolonging two adjacent sides of only one point, then to supplement the figure by points to obtain the missing additional sides. In the following diagrams, each additional layer is represented by a red point.

; Triangular numbers

; Square numbers

; Hexagonal numbers

If $c$ is the number on sides of a polygon, then the $c$-polygonal number of row $n$ correspondent is:

$\{1\; \backslash \; over\; 2\}\; \backslash \; N\; \backslash \; \backslash \; left\; (c-2)\; N\; (c-4)\; \backslash \; \backslash \; right$.

By convention 1 is the first polygonal number for any number on sides).

The electronic Encyclopédie of the whole continuations avoids the terms using of the Greek prefixes (such as for example, “octagonal”) and preferably uses terms using of the numerical prefixes (like “8-gonal”).

References

• The Penguin Dictionary off Curious and Interesting Numbers , David Wells (Penguin Books, 1997) 0140261494. (The Penguin dictionary of the curious and interesting numbers)

• polygonal numbers with MathWorld

Random links:

Darius Khondji | Canton of Savigny-the-Temple | Gottlob Frick | Benzaiten | The Community of communes of the Rhone to the gorges of Ardeche | Bayport,_la_Floride

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