Definition:Limaçon of Pascal/Shape

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