Normal tube
Encyclopedia
In topology
, a normal tube to a smooth
curve
is a manifold
defined as the union of all discs such that
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, a normal tube to a smooth
Smooth function
In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. Higher order differentiability classes correspond to the existence of more derivatives. Functions that have derivatives of all orders are called smooth.Most of...
curve
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...
is a manifold
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
defined as the union of all discs such that
- all the discs have the same fixed radius;
- the center of each disc lies on the curve; and
- each disc lies in a plane normalOrthogonalityOrthogonality occurs when two things can vary independently, they are uncorrelated, or they are perpendicular.-Mathematics:In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle...
to the curve where the curve passes through that disc's center.