In mathematics, a Cassini oval is a set of points in the plane such that each point p on the oval bears a special relation to two other, fixed points q₁ and q₂, namely that the product Main article: History of mathematics The evolution of mathematics can be seen to be an ever increasing series of abstractions. ... In mathematics, a set can be thought of as any well-defined collection of things considered as a whole. ... In mathematics, a plane is the fundamental two-dimensional object. ... An oval or ovoid was originally an egg shape (from Latin OVVM); it is now usually used to refer to ellipses, but can also mean any similar shape, such as egg shapes or race-course shapes (a semicircle on either side of a quadrilateral). ...

is constant. The points q₁ and q₂ are called the foci of the oval. In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ... The word focus (pl. ...

Cassini ovals are named after the astronomer Giovanni Domenico Cassini. Other names include Cassinian ovals and ovals of Cassini. Giovanni Domenico (Jean-Dominique) Cassini Giovanni Domenico Cassini (June 8, 1625 - September 14, 1712) was an Italian-French astronomer and engineer. ...

Denote the above constant product by b². Denote

The shape of the oval depends on the ratio b/a. When b/a is greater than 1, the locus is a single, connected loop. When b/a is less than 1, the locus comprises two disconnected loops. When b/a is equal to 1, the locus is a lemniscate. In mathematics, a locus (plural loci) is a collection of points which share a common property. ... In mathematics, a lemniscate is a type of curve described by a Cartesian equation of the form: Graphing this equation produces a curve similar to . ...

Some Cassini ovals. The foci are (-1, 0) and (1, 0). The curves are annotated with the value of b².