# Definition:Lemniscate of Bernoulli/Focus

Jump to navigation
Jump to search

## Definition

Consider the **lemniscate of Bernoulli** defined as the locus $M$ described by the equation:

- $P_1 M \times P_2 M = \paren {\dfrac {P_1 P_2} 2}^2$

Each of the two points $P_1$ and $P_2$ can be referred to as a **focus** of the lemniscate.

## Linguistic Note

The word **focus** is of Latin origin, hence its irregular plural form **foci**.

It was introduced into geometry by Johannes Kepler when he established his First Law of Planetary Motion. The word in Latin means **fireplace** or **hearth**, which is appropriate, considering the position of the sun.

The pronunciation of **foci** has a hard **c**, and is rendered approximately as ** folk-eye**.

Beware the solecism of pronouncing it ** fo-sigh**, which is incorrect.

## Sources

- Weisstein, Eric W. "Lemniscate." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Lemniscate.html