Definition:Lemniscate of Bernoulli/Focus

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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.