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Construction of the limaçon r = 2 + cos(π – θ) with polar coordinates' origin at (x, y) = ( 1 / 2 , 0). In geometry, a limaçon or limacon / ˈ l ɪ m ə s ɒ n /, also known as a limaçon of Pascal or Pascal's Snail, is defined as a roulette curve formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius.
The limaçon trisectrix specified as the polar equation = (+ ), where a > 0. When a < 0, the resulting curve is the reflection of this curve with respect to the line = / As a function, r has a period of 2π. The inner and outer loops of the curve intersect at the pole.
A limaçon is a conchoid with a circle as the given curve. The so-called conchoid of de Sluze and conchoid of Dürer are not actually conchoids. The former is a strict cissoid and the latter a construction more general yet.
There is a variety of such curves and the methods used to construct an angle trisector differ according to the curve. Examples include: Limaçon trisectrix (some sources refer to this curve as simply the trisectrix.) Trisectrix of Maclaurin; Equilateral trefoil (a.k.a. Longchamps' Trisectrix)
Circle — negative pedal curve of a limaçon. In geometry, a negative pedal curve is a plane curve that can be constructed from another plane curve C and a fixed point P on that curve. For each point X ≠ P on the curve C, the negative pedal curve has a tangent that passes through X and is perpendicular to line XP.
Limaçon. Cardioid; Limaçon trisectrix; Trifolium curve [citation needed] Degree 5. Quintic of l'Hospital [1] Degree 6. Astroid;
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In geometry, a Cartesian oval is a plane curve consisting of points that have the same linear combination of distances from two fixed points . These curves are named after French mathematician René Descartes , who used them in optics .