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 (OM0) such that , when M0 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.

© Robert FERRÉOL  2017