Editing Angle trisection (section)

==Uses of angle trisection==
[[File:01-Siebeneck-Tomahawk-Animation.gif|thumb|350px|
An animation of a neusis  construction of a [[heptagon]] with radius of [[circumcircle]] <math>\overline{OA} = 6</math>, based on [[Andrew M. Gleason]], using angle trisection by means of the tomahawk<ref name="Gleason"/>{{rp|p. 186}}]]
A [[cubic equation]] with real coefficients can be solved geometrically with compass, straightedge, and an angle trisector if and only if it has three [[real number|real]] [[root of a polynomial|roots]].<ref name="Gleason">{{cite journal|last=Gleason|first=Andrew Mattei|author-link=Andrew M. Gleason|title=Angle trisection, the heptagon, and the triskaidecagon |journal=The American Mathematical Monthly|date=March 1988|volume=95|issue=3 |pages=185–194|url=http://apollonius.math.nthu.edu.tw/d1/ne01/jyt/linkjstor/regular/1.pdf#3 |archive-url=https://web.archive.org/web/20141105205944/http://apollonius.math.nthu.edu.tw/d1/ne01/jyt/linkjstor/regular/7.pdf#3 |doi= 10.2307/2323624|archive-date=November 5, 2014 |url-status=dead|jstor=2323624}}</ref>{{rp|Thm. 1}}

A [[regular polygon]] with ''n'' sides can be constructed with ruler, compass, and angle trisector if and only if <math>n=2^r3^sp_1p_2\cdots p_k,</math> where ''r, s, k'' ≥ 0 and where the ''p''<sub>''i''</sub> are distinct primes greater than 3 of the form <math>2^t3^u +1</math> (i.e. [[Pierpont prime]]s greater than 3).<ref name="Gleason"/>{{rp|Thm. 2}}