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PARABOLIC TRIFOLIUM

Curve studied by G. de longchamps in 1888 (Loria p. 136)

 
Cartesian equation: .
Polar equation: .
Cartesian parametrization:  ().
Rational Cartesian parametrization:  ().
Rational quartic with triple point at O, and asymptotic parabola:  (hence the name).

Remark: just as the parabolic folium is not a folium, the parabolic trifolium is not a trifolium.
 
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© Robert FERRÉOL  2017