Conchoid of de Sluze

Cartesian equation:
a(x + a)(x² + y²) = k²x²
Polar equation:
a(r cos( theta ) + a) = k²cos²( theta )

Click below to see one of the Associated curves.

Definitions of the Associated curves Evolute

Involute 1 Involute 2

Inverse curve wrt origin Inverse wrt another circle

Pedal curve wrt origin Pedal wrt another point

Negative pedal curve wrt origin Negative pedal wrt another point

Caustic wrt horizontal rays Caustic curve wrt another point

If your browser can handle JAVA code, click HERE to experiment interactively with this curve and its associated curves.

This curve was first constructed by René de Sluze in 1662.

René Francois Walter- Baron de Sluze was an important man in the church as well as a mathematician. He contributed to the geometry of spirals and the finding of geometric means. He also invented a general method for determining points of inflection of a curve.

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JOC/EFR/BS January 1997

The URL of this page is:
http://www-history.mcs.st-andrews.ac.uk/history/Curves/Conchoidsl.html

Definitions of the Associated curves	Evolute
Involute 1	Involute 2
Inverse curve wrt origin	Inverse wrt another circle
Pedal curve wrt origin	Pedal wrt another point
Negative pedal curve wrt origin	Negative pedal wrt another point
Caustic wrt horizontal rays	Caustic curve wrt another point