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{{Even polygon db|Even polygon stat table|p10}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
[[File:Gonbad-e Qabus.JPG|thumb|[[Gonbad-e Qabus (tower)|Gonbad-e Qabus]], the tallest pure brick tower in the world, is built on a decagonal plan.]]
In [[geometry]], a '''decagon''' is any [[polygon]] with ten sides and ten [[angle]]s. A [[regular polygon|regular]] decagon has all sides of equal length and each internal angle equal to 144°. Its [[Schläfli symbol]] is {10}.


==Regular decagon==
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
The [[area]] of a regular decagon is: (with ''t'' = edge length)
* Only registered users will be able to execute this rendering mode.
:<math>A = \frac{5}{2}t^2 \cot \frac{\pi}{10} = \frac{5t^2}{2} \sqrt{5+2\sqrt{5}} \simeq 7.694208843 t^2.</math>
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


An alternative formula is <math>\scriptstyle A\,=\,2.5dt</math> where ''d'' is the distance between parallel sides, or the height when the decagon stands on one side as base.<br>
Registered users will be able to choose between the following three rendering modes:
By simple trigonometry <math>\scriptstyle d\,=\,2t(\cos{54^\circ}\,+\,\cos{18^\circ})</math>.


==Sides==
'''MathML'''
The side of a regular decagon inscribed in a unit circle is <math>\tfrac{-1+\sqrt{5}}{2}=\tfrac{1}{\phi}</math>, where ''&#x03D5;'' is the [[golden ratio]], <math>\tfrac{1+\sqrt{5}}{2}</math>.
:<math forcemathmode="mathml">E=mc^2</math>


===Construction===
<!--'''PNG'''  (currently default in production)
A regular decagon is [[constructible polygon|constructible]] using [[compass and straightedge]]:
:<math forcemathmode="png">E=mc^2</math>


[[File:Regular Decagon Inscribed in a Circle.gif|Construction of a regular decagon]]
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


An alternative (but similar) method is as follows:
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].
#Construct a pentagon in a circle by one of the methods shown in [[Pentagon#Construction_of_a_regular_pentagon|constructing a pentagon]].
#Extend a line from each vertex of the pentagon through the center of the [[circle]] to the opposite side of that same circle. Where each line cuts the circle is a vertex of the decagon.
#The five corners of the pentagon constitute alternate corners of the decagon. Join these points to the adjacent new points to form the decagon.


==Related figures==
==Demos==
There is one regular [[star polygon]], the [[decagram (geometry)|decagram]] {10/3}, using the same points, but connecting every third points. There are also two compounds: {10/4} is reduced to 2{5/2} as two [[pentagram]]s, and {10/2} is reduced to 2{5} as two [[pentagon]]s.


{| class=wikitable width=360
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
|- align=center
|[[File:Truncated pentagon.png|120px]]<BR>A [[truncation (geometry)|truncated]] regular pentagon
|[[File:Decagram_10_3.png|120px]]<br>{10/3}<BR>[[Decagram (geometry)|Decagram]]
|[[Image:Decagram 10 2.png|120px]]<br>{10/2} or 2{5}
|[[Image:Decagram 10 4.png|120px]]<br>{10/4} or 2{5/2}
|}


===Petrie polygons===
The regular decagon is the [[Petrie polygon]] for many higher dimensional polytopes, shown in these skew [[orthogonal projection]]s in various [[Coxeter plane]]s:


{| class=wikitable width=450
* accessibility:
|- align=center valign=top
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
!valign=center|A<sub>9</sub>
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
|[[File:9-simplex_t0.svg|100px]]<br>[[9-simplex]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
|[[File:9-simplex_t1.svg|100px]]<br>[[Rectified 9-simplex]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
|[[File:9-simplex_t2.svg|100px]]<br>[[Birectified 9-simplex]]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
|[[File:9-simplex_t3.svg|100px]]<br>[[Trirectified 9-simplex]]
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
|[[File:9-simplex_t4.svg|100px]]<br>[[Quadrirectified 9-simplex]]
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.
|- align=center valign=top
!valign=center|BC<sub>5</sub>
|[[File:5-cube_t4.svg|100px]]<br>[[5-orthoplex]]
|[[File:5-cube_t3.svg|100px]]<br>[[Rectified 5-orthoplex]]
|[[File:5-cube_t2.svg|100px]]<br>[[Birectified 5-cube]]
|[[File:5-cube_t1.svg|100px]]<br>[[Rectified 5-cube]]
|[[File:5-cube_t0.svg|100px]]<br>[[5-cube]]
|- align=center valign=top
!valign=center|D<sub>6</sub>
|[[File:6-cube_t5_B5.svg|100px]]<br>[[5-orthoplex|t<sub>1</sub>(4<sub>31</sub>)]]
|[[File:6-cube_t4_B5.svg|100px]]<br>[[Rectified 5-orthoplex|t<sub>3</sub>(1<sub>31</sub>)]]
|[[File:6-cube_t3_B5.svg|100px]]<br>[[Birectified 5-orthoplex|t<sub>2</sub>(1<sub>31</sub>)]]
|[[File:6-demicube_t1_D6.svg|100px]]<br>[[Rectified 6-demicube|t<sub>1</sub>(1<sub>31</sub>)]]
|[[File:6-demicube_t0_D6.svg|100px]]<br>[[6-demicube]]<br>(1<sub>31</sub>)
|- align=center valign=top
!valign=center|H<sub>3</sub>
|[[File:Dodecahedron petrie.png|100px]]<br>[[Dodecahedron]]
|[[File:Icosahedron petrie.png|100px]]<br>[[Icosahedron]]
|[[File:Dodecahedron t1 H3.png|100px]]<br>[[Icosidodecahedron]]
|}


==See also==
==Test pages ==
*[[decagonal number]]
*[[Gambrel]]
*[[Golden ratio]]


==External links==
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*{{MathWorld |urlname=Decagon |title=Decagon}}
*[[Displaystyle]]
*[http://www.mathopenref.com/decagon.html Definition and properties of a decagon] With interactive animation
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


{{Polygons}}
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
[[Category:Polygons]]
==Bug reporting==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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