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Relationships between the number of singularities of plane algebraic curves. Given a plane curve, m = n(n-1)-2delta-3kappa (1) n = m(m-1)-2tau-3iota (2) iota = ...

An area-preserving affine transformation. Equiaffinities include the crossed hyperbolic rotation, elliptic rotation, hyperbolic rotation, and parabolic rotation.

The modular equation of degree five can be written (u/v)^3+(v/u)^3=2(u^2v^2-1/(u^2v^2)).

A surface represented parametrically by elliptic functions.

An asymptote is a line or curve that approaches a given curve arbitrarily closely, as illustrated in the above diagram. The plot above shows 1/x, which has a vertical ...

A curve in two dimensions on which the value of a function f(x,y) is a constant. Other synonymous terms are equipotential curve, isarithm, and isopleth. A plot of several ...

A crunode, also known as an ordinary double point, of a plane curve is point where a curve intersects itself so that two branches of the curve have distinct tangent lines. ...

The distribution parameter of a noncylindrical ruled surface parameterized by x(u,v)=sigma(u)+vdelta(u), (1) where sigma is the striction curve and delta the director curve, ...

A set of curves whose equations are of the same form but which have different values assigned to one or more parameters in the equations. Families of curves arise, for ...

A ruled surface parameterization x(u,v)=b(u)+vg(u) is called noncylindrical if gxg^' is nowhere 0. A noncylindrical ruled surface always has a parameterization of the form ...