Definition:Lemniscate

Definition

Lemniscate of Bernoulli

Let $P_1$ and $P_2$ be points in the plane such that $P_1 P_2 = 2 a$ for some constant $a$.

The lemniscate of Bernoulli is the locus of points $M$ in the plane such that:

$P_1 M \times P_2 M = a^2$

Also see

• Results about lemniscates can be found here.

Linguistic Note

The word lemniscate comes from the Latin word lemniscus, which means pendant ribbon.

The word may ultimately derive from the Latin lēmniscātus, which means decorated with ribbons.

This may in turn come from the ancient Greek island of Lemnos where ribbons were worn as decorations.