Lemniscate of Bernoulli
In geometry, the lemniscate of Bernoulli is a plane curve whose shape resembles the numeral 8 or the ∞ symbol. It can be defined from two given points F 1 {\displaystyle F_{1}} and F 2 {\displaystyle F_{2}} , called the foci, as the locus of points P {\displaystyle P} satisfying the relation | P F 1 | ⋅ | P F 2 | = c 2 , {\displaystyle |PF_{1}|\cdot |PF_{2}|=c^{2},} where the notation | A B | {\displaystyle |AB|} means the distance between two points A {\displaystyle A} and B {\displaystyle B} , and c = 1 2 | F 1 F 2 | {\displaystyle c={\tfrac {1}{2}}|F_{1}F_{2}|} is half the distance between foci.