Nondeterministic finite automaton: Difference between revisions

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Closure properties: emphasize use of eps.-trns. / nondet. e.g. for union automaton construction
 
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{{Odd polygon db|Odd polygon stat table|p13}}
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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 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}}

Latest revision as of 11:14, 26 November 2014

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