Curvature
Curvature is a measure of the amount of bending of a curve or surface.
Curvature is a college-level concept that would be first encountered in a differential geometry course.
Examples
| Gaussian Curvature: |
Gaussian curvature is one type measure of the amount of "bending" a surface undergoes at a given point which is independent of the coordinate system used to describe it. |
| Mean Curvature: |
The mean curvature is the amount of "bending" of a surface at given point defined as the average of the two so-called "principal curvatures." |
Prerequisites
| Curve: |
A curve is a continuous map from a one-dimensional space to an n-dimensional space. Loosely speaking, the word "curve" is often used to mean the function graph of a two- or three-dimensional curve. |
| Derivative: |
A derivative is the infinitesimal rate of change in a function with respect to one of its parameters. |
| Surface: |
A surface is a two-dimensional piece of three-dimensional space. |
| Tangent Vector: |
A tangent vector is a vector pointing in the direction of the tangent line to the graph of a function. |
Classroom Articles on Differential Geometry (Up to College Level)
