Τετάρτη 28 Φεβρουαρίου 2024

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:  .
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