In polar coordinates, the limaçons drawn on the board revealed unexpected symmetries that fascinated the class.

In classical geometry, the limaçon generated by the polar equation ρ = a + b cos θ can appear as a dimpled curve, a loop, or — in the special case where a = b — a cardioid.

During the lecture, the professor sketched several limaçons of Pascal to illustrate different types of loops.

During the lecture, the professor sketched the limaçon of Pascal to illustrate a family of curves.