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CONCHOID
From the Greek Kogkhoeidês: similar to a shell.
Other name: conchoidal curve. 
Polar equation: where is the polar equation of the initial curve. 
The conchoid of a curve with pole O (or with respect to O) and modulus a (algebraic value) is the locus of the points M on the line (OM_{0}) such that , when M_{0} describes .
For example, the curve described by a dog pulling on its leash of length a in the direction of a cat located at O, when its master describes the curve , is the conchoid of this curve, with modulus –a. Or, consider a rigid bar sliding along a point O with one of its points constrained to describe the curve : all the points on the bar describe conchoids of . The general notion at play here is the glissette. Conchoids can also be physically obtained by a cylindrical anamorphosis.

This notion is also a special case of the cissoid.
Examples:
 conchoids of lines, or
conchoids of Nicomedes.
 conchoids of circles, including the limaçons of Pascal when the pole is on the circle.
 conchoids of roses.
 conchoids of right strophoids with respect to the summit of the loop are strophoids.
 conchoids of the Archimedean spiral with respect to its centre are isometric Archimedean spirals.
 conchoids of conics with respect to their focus, or Jerabek's curves.
Dürer's conchoids are of another kind.
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© Robert FERRÉOL 2017