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CONCHOID
From the Greek Kogkhoeidês: similar to a shell.
Other name: conchoidal curve. |
Polar equation: |
The conchoid of a curve 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 Or, consider a rigid bar sliding along a point O with one of its points constrained to describe the curve Conchoids can also be physically obtained by a cylindrical anamorphosis.
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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