Definition:Lemniscate of Bernoulli/Geometric Definition
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:
- $P_1 M \times P_2 M = a^2$
Each of the two points $P_1$ and $P_2$ can be referred to as a focus of the lemniscate.
Each of the two loops that constitute the lemniscate can be referred to as a lobe 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.
- Equivalence of Definitions of Lemniscate of Bernoulli
- Lemniscate of Bernoulli is Special Case of Ovals of Cassini
Source of Name
This entry was named for Jacob Bernoulli.
The lemniscate of Bernoulli was investigated in some depth by Jacob Bernoulli, from whom it was given its name.
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.
- 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,31102 87771 46059 90523 \ldots$
- Weisstein, Eric W. "Lemniscate." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Lemniscate.html