Difference between revisions of "Cubic Command"

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<noinclude>{{Manual Page|version=4.2}}</noinclude>  
 
<noinclude>{{Manual Page|version=4.2}}</noinclude>  
 
{{command|geometry}}
 
{{command|geometry}}
;Cubic[ <Point A>, <Point B>, <Point C>, <Index n> ]
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;Cubic[ <Point>, <Point>, <Point>, <Number> ]
:Gives ''n''-th [http://bernard.gibert.pagesperso-orange.fr/ctc.html triangle cubic] of triangle ''ABC''.
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:Gives ''n''-th [http://bernard.gibert.pagesperso-orange.fr/ctc.html triangle cubic] of the given triangle ''ABC''.
{{Note|This command is in development, set of supported ''n''  is changing.}}
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:{{example|1=<div>Let ''A = (0, 1)'', ''B = (2, 1)'' and ''C = (1, 2)''. <br><code><nowiki>Cubic[A, B, C, 2]</nowiki></code> yields the implicit curve ''x³ - 3x² - 5x y² + 14x y - 7x + 5y² - 14y = -9''.</div>}}
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{{Note|This command is in development, set of supported index ''n''  is changing.}}
 
==Some common triangle cubics==
 
==Some common triangle cubics==
 
{| class=pretty
 
{| class=pretty

Revision as of 14:13, 3 September 2013



Cubic[ <Point>, <Point>, <Point>, <Number> ]
Gives n-th triangle cubic of the given triangle ABC.
Example:
Let A = (0, 1), B = (2, 1) and C = (1, 2).
Cubic[A, B, C, 2] yields the implicit curve x³ - 3x² - 5x y² + 14x y - 7x + 5y² - 14y = -9.
Note: This command is in development, set of supported index n is changing.

Some common triangle cubics

Index n Cubic
1 Neuberg Cubic
2 Thomson Cubic
3 McCay Cubic
4 Darboux Cubic
5 Napoleon/Feuerbach Cubic
7 Lucas Cubic
17 1st Brocard Cubic
18 2nd Brocard Cubic

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