TORPEDO CURVE Curve studied by G. Gohierre de Longchamps in 1884 (geometrie analytique, tome 2, 511-515). Homemade name (G. de Longchamps called this curve the right trifolium, but this name now refers to a more general family).  Polar equation: . Cartesian equation: . Cartesian parametrization: ( ). Complex parametrization: . Rational quartic. In a frame turned by p/4: Polar equation: . Cartesian equation: .

 The torpedo is the strophoid of a circle (here the circle with centre (a/4, 0) passing by O) with respect to a point O on the circle and a point A located at infinity in the direction of the diameter passing by O. See also, on this page, a beautiful animation of another construction of the torpedo, mistakenly called Cartesian folium. It is also a special case of right trifolium (pedal of a deltoid with respect to the point on the inscribed circle that is the symmetric image of the vertex of the deltoid - see folium), of "fish curve" and of tritrochoid (cf the complex parametrization). It is the locus of the isobarycentre of 3 circular motions with same radius, two of which have opposite speeds while the other has double speed. Like all "fish" curves, the torpedo is a planar projection of Viviani's window. It can also be obtained as the orthopolar of a circle.

See equilateral trefoil for a succinct study of its inverse.

A very close variation of the torpedo is called the "Cramer trifolium": Cartesian equation: . Polar equation: .

Who knows why certain mathematicians studied variations of the torpedo and called them "dickoids":   Tardy dickoid    