Nondeterministic finite automaton: Difference between revisions
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{{Odd polygon db|Odd polygon stat table|p13}} | |||
In [[geometry]], a '''tridecagon''' (or '''triskaidecagon''') is a [[polygon]] with 13 sides and angles. | |||
==Regular tridecagon== | |||
The measure of each internal angle of a [[Regular polygon|regular]] tridecagon is approximately 152.308 [[degree (angle)|degree]]s, and the area with side length ''a'' is given by | |||
:<math>A = \frac{13}{4}a^2 \cot \frac{\pi}{13} \simeq 13.1858\,a^2.</math> | |||
===Numismatic use=== | |||
The regular tridecagon is used as the shape of the [[Coins of the Czech koruna|Czech 20 korun coin]].<ref>Colin R. Bruce, II, George Cuhaj, and Thomas Michael, ''2007 Standard Catalog of World Coins'', Krause Publications, 2006, ISBN 0896894290, p. 81.</ref> | |||
==Related polygons== | |||
A tridecagram is a 13-sided [[star polygon]]. There are 5 regular forms given by [[Schläfli symbol]]s: {13/2}, {13/3}, {13/4}, {13/5}, {13/6}. | |||
:[[Image:Triskaidecagrams.svg|360px]] | |||
==Construction== | |||
A regular tridecagon is not [[constructible polygon|constructible]] with [[compass and straightedge]]. However, it is constructible using a [[Neusis construction]].<ref>{{citation | |||
| last = Gleason | first = Andrew M. | authorlink = Andrew Gleason | |||
| doi = 10.2307/2323624 | |||
| issue = 3 | |||
| journal = [[American Mathematical Monthly]] | |||
| mr = 935432 | |||
| pages = 185–194 | |||
| title = Angle trisection, the heptagon, and the triskaidecagon | |||
| volume = 95 | |||
| year = 1988}}.</ref> | |||
===Petrie polygons=== | |||
The regular tridecagon is the [[Petrie polygon]] for a number of higher dimensional polytope, projected in a skew [[orthogonal projection]], including from the A<sub>12</sub>, [[12-simplex]] family: | |||
{| class=wikitable width=750 | |||
|- align=center | |||
!A<sub>12</sub> | |||
|[[File:12-simplex t0.svg|125px]]<br>[[12-simplex]] | |||
|[[File:12-simplex t1.svg|125px]]<br>[[Rectified 12-simplex]] | |||
|[[File:12-simplex t2.svg|125px]]<br>[[Birectified 12-simplex]] | |||
|[[File:12-simplex t3.svg|125px]]<br>[[trirectified 12-simplex]] | |||
|[[File:12-simplex t4.svg|125px]]<br>[[quadrirectified 12-simplex]] | |||
|[[File:12-simplex t5.svg|125px]]<br>[[quintirectified 12-simplex]] | |||
|} | |||
==References== | |||
{{reflist}} | |||
==External links== | |||
*{{MathWorld |title=Tridecagon |urlname=Tridecagon}} | |||
{{Polygons}} | |||
[[Category:Polygons]] | |||
{{Elementary-geometry-stub}} | |||
Revision as of 19:29, 27 January 2014
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In geometry, a tridecagon (or triskaidecagon) is a polygon with 13 sides and angles.
Regular tridecagon
The measure of each internal angle of a regular tridecagon is approximately 152.308 degrees, and the area with side length a is given by
Numismatic use
The regular tridecagon is used as the shape of the Czech 20 korun coin.[1]
Related polygons
A tridecagram is a 13-sided star polygon. There are 5 regular forms given by Schläfli symbols: {13/2}, {13/3}, {13/4}, {13/5}, {13/6}.
Construction
A regular tridecagon is not constructible with compass and straightedge. However, it is constructible using a Neusis construction.[2]
Petrie polygons
The regular tridecagon is the Petrie polygon for a number of higher dimensional polytope, projected in a skew orthogonal projection, including from the A12, 12-simplex family:
| A12 |  12-simplex |
 Rectified 12-simplex |
 Birectified 12-simplex |
 trirectified 12-simplex |
 quadrirectified 12-simplex |
 quintirectified 12-simplex |
|---|
References
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Template:Elementary-geometry-stub
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