Lemniscate - Wikipedia The lemniscate of Bernoulli and its two foci In algebraic geometry, a lemniscate ( l ɛ m ˈ n ɪ s k ɪ t or ˈ l ɛ m n ɪ s ˌ k eɪ t,-k ɪ t ) [1] is any of several figure-eight or ∞-shaped curves
Lemniscate -- from Wolfram MathWorld The lemniscate, also called the lemniscate of Bernoulli, is a polar curve defined as the locus of points such that the product of distances from two fixed points (-a,0) and (a,0) (which can be considered a kind of foci with respect to multiplication instead of addition) is a constant a^2
Lemniscate - MIT OpenCourseWare The curve described in 2polar coordinates by r = cos(2θ) is called a lemniscate a) For what values of θ does there exist such a point (r, θ)? b) For what values of θ is r at its minimum length?
Lemniscate of Bernoulli - Interactive Mathematics Jacob Bernoulli (1655 - 1755) was a brilliant Swiss mathematician who discovered and developed a broad range of mathematical concepts, including the value of e, differential equations and number theory He described what's now called the Lemniscate of Bernoulli in 1694 as a modification of the Ellipse
Lemniscates - Encyclopedia of Mathematics A lemniscate is a level curve of a polynomial If all the foci $F_k$: $z_k=x_k+iy_k$, $k=1,\dotsc,n$, are distinct and the radius of the lemniscate is sufficiently small, then the lemniscate consists of $n$ continua that have pairwise no common points
Lemniscate - Michigan State University The general properties of the lemniscate were discovered by G Fagnano in 1750 (MacTutor Archive) Gauss's and Euler's investigations of the Arc Length of the curve led to later work on Elliptic Functions