Limaçon Evolute

Limacon Evolute

The limaçon evolute is the catacaustic of a circle for a radiant point. It has parametric equations

			(1)
			(2)

For , one complete parameter period is bounded when either or . In these regimes, its signed area is

(3)

(E. Weisstein, Sep. 23, 2026). This is the signed area of the standard traversal, so it records the curve orientation and multiplicity and is not in general the area of the union of the bounded regions. When , the denominators in the parametric equations vanish during the period, so the bounded-traversal formula does not apply. The boundary cases and are also excluded.