A curve shaped like the figure eight (see illus.), referred to by Jacques Bernoulli in 1694. Let F₁, F₂ be points of a plane π, with F₁F₂ = 2a, a > 0. The locus of a point P of π which moves so that PF₁ · PF₂ = b², where b is a positive constant, is called an oval of Cassini. The lemniscate is obtained when   b = a. Its equation in rectangular coordinates is (x² + y²)² = a²(x² − y²) and in polar coordinates ρ² = a² cos 2θ. It is the locus of the point of intersection of a variable tangent to a rectangular hyperbola with the line through the center perpendicular to the tangent. The area enclosed by the lemniscate ρ² = a² cos 2θ is a².