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Instant-use add-on functions for the Wolfram Language
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Get the Lucas cubic curve of a triangle
ResourceFunction["LucasCubic"][{p1,p2,p3},{x,y}] returns the Lucas cubic curve. |
Find the Lucas cubic of three triangle vertices:
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Visualize the cubic curve:
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The Lucas cubic is closely related to the Thomson cubic:
Degenerated triangle is not supported:
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The circumcenter, orthocenter and Gergonne point and Nagel point of the reference triangle are on the Lucas cubic. The vertices of the reference triangle and that of its anticomplementary triangle are also on the cubic:
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Direct computation of three asymptotes:
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Solve for y in terms of x:
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Extract the constant term and the linear term for each result:
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Visualize the curve and its asymptotes:
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Or we can wrap everything into a Manipulate function:
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