Search results
Results from the WOW.Com Content Network
The curve of intersection of the plane and the surface has zero curvature at that point. An asymptotic curve is a curve such that, at each point, the plane tangent to the surface is an osculating plane of the curve.
Let A : (a,b) → R 2 be a parametric plane curve, in coordinates A(t) = (x(t),y(t)), and B be another (unparameterized) curve. Suppose, as before, that the curve A tends to infinity. The curve B is a curvilinear asymptote of A if the shortest distance from the point A(t) to a point on B tends to zero as t → b.
An asymptote is a straight line that a curve approaches but never meets or crosses. Informally, one may speak of the curve meeting the asymptote "at infinity" although this is not a precise definition. In the equation =, y becomes arbitrarily small in magnitude as x increases.
A space curve is a curve for which is at least three-dimensional; a skew curve is a space curve which lies in no plane. These definitions of plane, space and skew curves apply also to real algebraic curves , although the above definition of a curve does not apply (a real algebraic curve may be disconnected ).
In graph theory, a branch of mathematics, an undirected graph is called an asymmetric graph if it has no nontrivial symmetries.. Formally, an automorphism of a graph is a permutation p of its vertices with the property that any two vertices u and v are adjacent if and only if p(u) and p(v) are adjacent.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The curve β is uniquely determined up to a special affine transformation. This is analogous to the fundamental theorem of curves in the classical Euclidean differential geometry of curves , in which the complete classification of plane curves up to Euclidean motion depends on a single function κ , the curvature of the curve.
For a surface defined in 3D space, the mean curvature is related to a unit normal of the surface: = ^ where the normal chosen affects the sign of the curvature. The sign of the curvature depends on the choice of normal: the curvature is positive if the surface curves "towards" the normal.