Definition:Limaçon of Pascal/Shape

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Definition

Let $L$ denote a limaçon of Pascal.

Depending on the value of $b$, the shape of $L$ is as follows:

For $b \ge 2 a$, $L$ is wholly convex.
For $a < b < 2 a$, $L$ has a concavity.
For $b = a$, $L$ degenerates to a cardioid.
For $0 < b < a$, $L$ has a loop inside its generating circle.
For $b = \dfrac a 2$, the internal loop of $L$ passes through the center of the generating circle.
For $b = 0$, $L$ degenerates to a circle.
For $b < 0$, $L$ is the same curve as for $-b$.
Limacon-of-Pascal-3.png Limacon-of-Pascal-2.png Limacon-of-Pascal-1-2.png Limacon-of-Pascal-1.png Limacon-of-Pascal-0-8.png Limacon-of-Pascal-0-5.png Limacon-of-Pascal-0-2.png Limacon-of-Pascal-0.png


Sources

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