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lemniscate    
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  • 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 Definition Meaning - Merriam-Webster
    The meaning of LEMNISCATE is a figure-eight shaped curve whose equation in polar coordinates is ρ2=a2 cos 2θ or ρ2=a2 sin 2θ
  • 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
  • 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?
  • 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
  • Lemniscate - Virtual Math Museum
    Lemniscate * The Lemniscate is a figure-eight curve with a simple me-chanical construction attributed to Bernoulli: Choose two ’focal’ points F 1,F 2 at distance L:= 2∗dd, then take three rods, one of length L, two of length R = L √ 2 The short ones can rotate around the focal points and the long one connects their free ends with
  • Lemniscate of Bernoulli - Wikipedia
    In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F 1 and F 2, known as foci, at distance 2c from each other as the locus of points P so that PF 1 ·PF 2 = c 2 The curve has a shape similar to the numeral 8 and to the ∞ symbol
  • 33 Facts About Lemniscate
    A lemniscate is a mathematical symbol shaped like a figure-eight or an infinity sign (∞) This intriguing shape has fascinated mathematicians, artists, and even philosophers for centuries Its name comes from the Latin word "lemniscus," meaning ribbon, which perfectly describes its looping form





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