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  • Lemniscate - Wikipedia
    The lemniscate may be defined as an algebraic curve, the zero set of the quartic polynomial when the parameter d is negative (or zero for the special case where the lemniscate becomes a pair of externally tangent circles)
  • 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 - MIT OpenCourseWare
    Lemniscate The curve described in polar coordinates by r2 = 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? c) For what values of θ is r at its maximum 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
  • Lemniscate - HandWiki
    The lemniscate may be defined as an algebraic curve, the zero set of the quartic polynomial (x 2 + y 2) 2 − c x 2 − d y 2 when the parameter d is negative (or zero for the special case where the lemniscate becomes a pair of externally tangent circles)
  • 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
  • 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
  • Introduction HILBERT’S LEMNISCATE THEOREM FOR
    lemniscate A topological annulus is a subset of bC homeomorphic to a Euclidean annulus {z : 1 ≤ |z| ≤ r} for some (and hence every) 1 < r ≤ ∞ A Jordan curve γ ⊂ bC is a homeomorphic image of T := {z : |z| = 1}, and γ is said to separate the two boundary components of a topological annulus A if each component of bC\γ contains





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