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The butterfly curve is a transcendental plane curve discovered by Temple H. Fay of University of Southern Mississippi in 1989. [1] Equation
Here for a curve, C, what matters is the point set (typically in the plane) underlying C, not a given parametrisation. For example, the unit circle is an algebraic curve (pedantically, the real points of such a curve); the usual parametrisation by trigonometric functions may involve those transcendental functions , but certainly the unit circle ...
1.2 Transcendental curves. 1.3 Piecewise constructions. ... Butterfly curve (algebraic) (genus 7) Curve families with variable genus. Polynomial lemniscate;
Butterfly curve (transcendental), a curve based on sine functions This page was last edited on 28 September 2016, at 06:40 (UTC). Text is available under the Creative ...
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In mathematics, the algebraic butterfly curve is a plane algebraic curve of degree six, given by the equation x 6 + y 6 = x 2 . {\displaystyle x^{6}+y^{6}=x^{2}.} The butterfly curve has a single singularity with delta invariant three, which means it is a curve of genus seven.
Toggle Transcendental curves subsection. 2.1 Spirals. 3 Piecewise constructions. ... Butterfly curve (algebraic) Elkies trinomial curves. Hyperelliptic curve. Klein ...
Quartic Plane Curve: Rational Curves: Degree 2: Conic Section(s) Unit Circle: Unit Hyperbola: Degree 3: Folium of Descartes: Cissoid of Diocles: Conchoid of de Sluze: Right Strophoid: Semicubical Parabola: Serpentine Curve: Trident Curve: Trisectrix of Maclaurin: Tschirnhausen Cubic: Witch of Agnesi: Degree 4: Ampersand Curve: Bean Curve ...