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The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change of the curve's osculating plane. The torsion tau is ...

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 ...

Relates invariants of a curve defined over the integers. If this inequality were proven true, then Fermat's last theorem would follow for sufficiently large exponents. ...

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 ...

Given a source S and a curve gamma, pick a point on gamma and find its tangent T. Then the locus of reflections of S about tangents T is the orthotomic curve (also known as ...

The pedal coordinates of a point P with respect to the curve C and the pedal point O are the radial distance r from O to P and the perpendicular distance p from O to the line ...