A plane quartic curve also called the cross curve or policeman on point duty curve (Cundy and Rollett 1989). It is given by the implicit equation (1) which is equivalent to (2) and (3) In...
A curve with polar coordinates, (1) studied by the Greek mathematician Nicomedes in about 200 BC, also known as the cochloid. It is the locus of points a fixed distance away from a line as measured along...
The Cassini ovals are a family of quartic curves, also called Cassini ellipses, described by a point such that the product of its distances from two fixed points a distance apart is a constant . The shape of the curve depends on...
The "Cartesian ovals," sometimes also known as the Cartesian curve or oval of Descartes, are the quartic curve consisting of two ovals. They were first studied by Descartes in 1637 and by Newton while classifying cubic curves. It...
The curve given by the polar equation (1) sometimes also written (2) where . The cardioid has Cartesian equation (3) and the parametric equation s (4) (5) The cardioid is a...
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 ...
