Intrinsic equation

Intrinsic equation

In geometry, an intrinsic equation of a curve is an equation that defines the curve using a relation between the curve's intrinsic properties, that is, properties that do not depend on the location and possibly the orientation of the curve. Therefore an intrinsic equation defines the shape of the curve without specifying its position relative to an arbitrarily defined coordinate system.

The intrinsic quantities used most often are arc length, tangential angle, curvature or radius of curvature, and, for 3-dimensional curves, torsion. Specifically:
* The Whewell equation is obtained as a relation between arc length and tangential angle.
* The Cesàro equation is obtained as a relation between arc length and curvature.

References

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External links

*MathWorld |title=Intrinsic Equation |urlname=IntrinsicEquation


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