Definition:Polygon/Regular
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Definition
A regular polygon is a polygon which is both equilateral and equiangular.
That is, in which all the sides are the same length, and all the vertices have the same angle:
Also known as
In Euclid's The Elements, a regular polygon is referred to as an equilateral and equiangular polygon.
Examples
Specific instances of regular polygons with specific numbers of sides are as follows:
- $3$ sides: Equilateral Triangle
- $4$ sides: Square
- $5$ sides: Regular Pentagon
- $6$ sides: Regular Hexagon
- $7$ sides: Regular Heptagon
- $8$ sides: Regular Octagon
- $9$ sides: Regular Nonagon or Regular Enneagon
- $10$ sides: Regular Decagon
- $11$ sides: Regular Hendecagon or Regular Undecagon
- $12$ sides: Regular Dodecagon
- $17$ sides: Regular Heptadecagon
The term regular $n$-gon is usually used nowadays to specify a regular polygon with a specific number, that is $n$, sides.
The specific name is usually invoked only in order to draw attention to the fact that such a regular polygon has a particularly interesting set of properties.
Also see
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{IV}$: The Prince of Amateurs
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.4$: Euclid (flourished ca. $300$ B.C.)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: polygon
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: regular polygon