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[[Image:Eudoxus.png|thumb|Graph of Kampyle of Eudoxus]]The '''Kampyle of Eudoxus''' ([[Ancient Greek|Greek]]: καμπύλη [γραμμή], meaning simply "curved [line], curve") is a [[curve]], with a [[Cartesian equation]] of
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


:<math>x^4=x^2+y^2</math>
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]]
* 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.


from which the solution ''x'' = ''y'' = 0 should be excluded, or, in [[polar coordinates]],
Registered users will be able to choose between the following three rendering modes:


:<math>r= \sec^2\theta\,.</math>
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


This quartic curve was studied by the Greek astronomer and mathematician [[Eudoxus of Cnidus]] (c. 408 BC – c.347 BC) in relation to the classical problem of [[doubling the cube]].
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


The Kampyle is symmetric about both the <math>x</math>- and <math>y</math>-axes.  It crosses the <math>x</math>-axis at <math>(-1,0)</math> and <math>(1,0)</math>.  It has [[inflection points]] at
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


:<math>(\pm\sqrt{3/2},\pm\sqrt{3}/2)</math>
<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].


(four inflections, one in each quadrant).  The top half of the curve is asymptotic to <math>x^2-\frac12</math> as <math>x \to \infty</math>, and in fact can be written as
==Demos==


:<math>y = x^2\sqrt{1-x^{-2}} = x^2 - \frac12 \sum_{n \ge 0} C_n(2x)^{-2n}</math>
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


where


:<math>C_n = \frac1{n+1} \binom{2n}{n}</math>
* accessibility:
** 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]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** 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]].
** 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]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


is the <math>n</math>th [[Catalan number]].
==Test pages ==


==See also==
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
* [[List of curves]]
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


==References==
*[[Inputtypes|Inputtypes (private Wikis only)]]
* {{cite book | author=J. Dennis Lawrence | title=A catalog of special plane curves | publisher=Dover Publications | year=1972 | isbn=0-486-60288-5 | pages=141–142 }}
*[[Url2Image|Url2Image (private Wikis only)]]
 
==Bug reporting==
==External links==
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 .
* {{MacTutor|class=Curves|id=Kampyle|title=Kampyle of Eudoxus}}
* {{MathWorld|urlname=KampyleofEudoxus|title=Kampyle of Eudoxus}}
 
{{geometry-stub}}
 
[[Category:Curves]]
 
[[ca:Càmpila d'Eudoxe]]
[[nl:Kampyle van Eudoxus]]
[[sl:Evdoksova kampila]]

Latest revision as of 23:52, 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


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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