The application for which Eisenstein developed his criterion was establishing the irreducibility of certain polynomials with coefficients in the Gaussian integers that arise in the study of the division of the lemniscate into pieces of equal arc-length.
32.
The equation of a hyperbola; since inversion is a birational transformation and the hyperbola is a rational curve, this shows the lemniscate is also a rational curve, which is to say a curve of genus zero.
33.
The ErdQs lemniscate has three ordinary " n "-fold points, one of which is at the origin, and a inverting the ErdQs lemniscate in the unit circle, one obtains a nonsingular curve of degree " n ".
34.
The ErdQs lemniscate has three ordinary " n "-fold points, one of which is at the origin, and a inverting the ErdQs lemniscate in the unit circle, one obtains a nonsingular curve of degree " n ".
35.
The Guardian's New Music critic, Michael Cragg, reviewed the album's track " Open Your Mind " in October 2012, while " Lemniscate " as a whole was featured as Rough Trade's " Album Of The Week " shortly after its release.
36.
The first, used in calculus, he called the variable finite, or potential infinite, represented by the \ infty sign ( known as the lemniscate ), and the actual infinite, which Cantor called the " true infinite . " His notion of transfinite arithmetic became the standard system for working with infinity within set theory.
37.
If " oval " means " continuous convex curve ", then there are counterexamples, such as triangles or one of the lobes of Huygens lemniscate " y " 2 = " x " 2 & minus; " x " 4, while pointed that if " oval " means " infinitely differentiable convex curve " then Newton's claim is correct and his argument has the essential steps of a rigorous proof.
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