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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 ...

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 ...

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.

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 dumbbell curve is the sextic curve a^4y^2=x^4(a^2-x^2). (1) It has area A=1/4pia^2 (2) and approximate arc length s approx 5.541a. (3) For the parametrization x = at (4) ...

A curve which intersects some straight line in an infinity of points (but for which not every point lies on this curve).

A curve which has at least multiplicity r_i-1 at each point where a given curve (having only ordinary singular points and cusps) has a multiplicity r_i is called the adjoint ...