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The order of the polynomial defining an algebraic curve.

A curve has positive orientation if a region R is on the left when traveling around the outside of R, or on the right when traveling around the inside of R.

A curve whose centrode revolves about a fixed axis with constant angle and speed when the curve is traversed with unit speed. The tangent indicatrix of a curve of constant ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

The quartic surface resembling a squashed round cushion on a barroom stool and given by the equation z^2x^2-z^4-2zx^2+2z^3+x^2-z^2 -(x^2-z)^2-y^4-2x^2y^2-y^2z^2+2y^2z+y^2=0.

A cusp is a point at which two branches of a curve meet such that the tangents of each branch are equal. The above plot shows the semicubical parabola curve x^3-y^2=0, which ...

A cusp catastrophe is a catastrophe which can occur for two control factors and one behavior axis. The cusp catastrophe is the universal unfolding of the singularity f(x)=x^4 ...

A cusp form is a modular form for which the coefficient c(0)=0 in the Fourier series f(tau)=sum_(n=0)^inftyc(n)e^(2piintau) (1) (Apostol 1997, p. 114). The only entire cusp ...

The function f(x)=1-2|x|^(1/2) for x in [-1,1]. The natural invariant is rho(y)=1/2(1-y).