EisatoponAI: CISSOID OF DIOCLES

Curve studied by Diocles, 180 BC; Fermat; Huygens.
From the Greek Kissos: ivy, probably in reference to the nervures...

Diocles (2nd century BC): Greek mathematician.

Polar equation:

.
Cartesian equation:

(the curve

is studied here).
Rational circular cubic with a cuspidal point.
Rational Cartesian parametrization:

, i.e.

(where t = tanq).
Cartesian tangential angle:

.
Curvilinear abscissa:

.
Radius of curvature:

.
Area between the curve and its asymptote:

EisatoponAI