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The quartic curve given by the implicit equation (x^2-a^2)(x-a)^2+(y^2-a^2)^2=0, (1) so-named because of its resemblance to a tooth. The bicuspid curve has cusps at (a,-a) ...

There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

A general plane quartic curve is a curve of the form (1) Examples include the ampersand curve, bean curve, bicorn, bicuspid curve, bifoliate, bifolium, bitangent-rich curve, ...

The stirrup curve is the quartic curve given by the equation (x^2-1)^2=y^2(y-1)(y-2)(y+5).

An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in K. A nonsingular algebraic curve is an algebraic curve ...

There are a few plane curves known as "bean curves." The bean curve identified by Cundy and Rowllet (1989, p. 72) is the quartic curve given by the implicit equation ...

A quintic curve is an algebraic curve of order five. Examples of quintic curves include the Burnside curve, butterfly catastrophe curve, and stirrup curve.

An algebraic curve of degree six. Examples include the astroid, atriphtaloid, Cayley's sextic, cornoid, cycloid of Ceva, dumbbell curve, ellipse evolute, epicycloid, Freeth's ...

The pedal of a curve C with respect to a point O is the locus of the foot of the perpendicular from O to the tangent to the curve. More precisely, given a curve C, the pedal ...

An octic curve is an algebraic curve of order eight. The pear curve is an example of an octic curve.