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Curvature

Explore Curvature on MathWorld


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)

  • Differential Geometry
  • Differential k-Form