Difference between revisions of "Cubic Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude> {{command|geometry}}
 
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;Cubic( <Point>, <Point>, <Point>, <Number> )
 
;Cubic( <Point>, <Point>, <Point>, <Number> )
:Gives ''n''-th [http://bernard.gibert.pagesperso-orange.fr/ctc.html triangle cubic] of the given triangle ''ABC''.
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:Gives ''n''-th [https://bernard-gibert.pagesperso-orange.fr/ctc.html triangle cubic] of the given triangle ''ABC''.
 
:{{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>}}
 
:{{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>}}
 
{{Note|This command is in development, set of supported index ''n''  is changing.}}
 
{{Note|This command is in development, set of supported index ''n''  is changing.}}

Latest revision as of 11:41, 15 June 2022


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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