Cochleoid

Polar equation:
r = a sin(θ)/θ


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.

The name means the snail-form curve. It was discussed by J Peck in 1700. The form given here is due to a Belgium Joseph Neuberg. The name originated in 1884 with writers Benthan and Falkenburg.

The points of contact of parallel tangents to the cochleoid lie on a strophoid.

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JOC/EFR/BS January 1997

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