Definition:Lemniscate of Bernoulli/Polar Definition
- $r^2 = 2 a^2 \cos 2 \theta$
Each of the two points $P_1$ and $P_2$ can be referred to as a focus of the lemniscate.
The line $P_1 P_2$ is the major axis of the lemniscate.
Each of the lines $O P_1$ and $O P_2$ is a major semiaxis of the lemniscate.
- $r^2 = a^2 \cos 2 \theta$
which is the same but for a scale factor:
Source of Name
This entry was named for Jacob Bernoulli.
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.