A quartic curve that resembles the symbol for the zodiacal sign Capricorn given by the implicit equation where , . The curve plotted above corresponds to , . This curve has a tacnode at the origin and a crunode...
There are two curves known as the butterfly curve. The first is the sextic plane curve given by the implicit equation (1) (Cundy and Rollett 1989, p. 72; left figure). The total area of both...
A quartic curve with implicit equation (1) or (2) and . In parametric form, (3) (4) The curvature is (5) REFERENCES: Lawrence, J. D. A Catalog of Special Plane Curves. New...
The quartic with implicit equation (1) The bow has vertical tangents at and horizontal tangents at . Its curvature is implicitly given by (2) The area enclosed by the two loops is given by (3) ...
A bitangent is a line that is tangent to a curve at two distinct points. There exist plane quartic curves that have 28 real bitangents (Shioda 1995, Trott 1997), for example ...
The bifolium is a folium with . The bifolium is a quartic curve and is given by the implicit equation is (1) and the polar equation (2) The bifolium has area (3) (4) (5) Its arc...
The bifoliate is the quartic curve given by the Cartesian equation (1) and the polar equation (2) for . It has a cusp at the origin . The area of the bifoliate is given by (3) (4) (5)...
The quartic curve given by the implicit equation (1) so-named because of its resemblance to a tooth. The bicuspid curve has cusps at and . The horizontal tangents are located at , and the vertical tangents at , , and...
The quartic curve given by the implicit equation (1) It has horizontal asymptotes at and vertical asymptotes at and The area enclosed by the curve is given by (2) (3) (Sloane's A193505). The...
