Conchoid by de Sluze for various
The de Sluze conchoid is a family of flat curves that was examined by René François Walther de Sluze in 1662 . In polar coordinates it is expressed as follows:
- The secant is the reciprocal function of the cosine .
The following applies to Cartesian coordinates :
However, the Cartesian form has for a solution point that does not exist in the polar coordinate form.
These expressions have an asymptote (for ). The point furthest from the asymptote a is . In curves intersect for yourself.
The area between the curve and the asymptote is calculated as follows:
-
For
-
For
The area of the loop is
-
For
Four curves of the family have special names:
Web links