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[[Image:PentagonConstruction.jpg|thumb|right|450px|A rather interesting straightedge-and-compass construction of a regular pentagon (shown in yellow)]]
A '''regular polygon''' is a [[polygon]] where all the [[side]]s and included [[angle]]s are [[equal]]. Examples include the [[equilateral triangle]] and the [[square]].
A '''regular polygon''' is a [[polygon]] where all the [[side]]s and included [[angle]]s are [[equal]]. Examples include the [[equilateral triangle]] and the [[square]].
===Construction of Regular Polygons===
===Construction of Regular Polygons===
In order to explain Gauss's Theorem, we need to understand about Fermat numbers, which are defined as numbers of the form 2<sup>2<sup>n</sup></sup>+1 where n is natural number or zero. The first 5 Fermat numbers are: 3, 5, 17, 257, 65537 <ref> Note that all of these are prime and Fermat conjectured in 1640 that all the Fermat numbers are prime. Rather surprisingly it wasn't until 1732 that Euler pointed out that the next Fermat number 4294967297 is not prime. It is divisible by 641. In fact the first 5 are the only know prime Fermat numbers and it seems reasonable that there are no others</ref>.
In order to explain Gauss's Theorem, we need to understand about Fermat numbers, which are defined as numbers of the form 2<sup>2<sup>n</sup></sup>+1,
where n is natural number or zero. The first 5 Fermat numbers are: 3, 5, 17, 257, 65537 <ref> Note that all of these are prime and Fermat conjectured in 1640 that all the Fermat numbers are prime. Rather surprisingly it wasn't until 1732 that Euler pointed out that the next Fermat number 4294967297 is not prime. It is divisible by 641. In fact the first 5 are the only know prime Fermat numbers and it seems reasonable that there are no others</ref>.