Examples for

Curvature

Curvature is a value equal to the reciprocal of the radius of the circle or sphere that best approximates the curve at a given point. This can be computed for functions and parameterized curves in various coordinate systems and dimensions. Related properties, such as the radius of curvature and center of curvature, are also easily computed by Wolfram|Alpha.
Curvature

Compute curvature for functions and curves in various coordinate systems.

Compute the curvature of a plane curve at a point:

curvature of y=x^2 at x=0.2

Specify the curve in polar form:

curvature of the polar curve r=t^3+2 near t=1/10

Compute the curvature of a space curve:

what is the curvature of (s, sin s, cos s) at s=2

Compute a curvature in higher dimensions:

curvature of {x(t)=t, y(t)=t^4, z(t)=t^2, w(t)=t} at t=1

Compute the curvature at an arbitrary point:

curvature of sin(x)

Compute an osculating circle:

osculating circle to (2cos[t], sin[t]) at t=pi/3

Compute a center of curvature:

center of curvature of y=e^(-x^2) at x=0

Compute a radius of curvature:

radius of curv. of {a sin(t), a t} at t=1
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