PARABOLIC TRIFOLIUM
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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