Whewell equation

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The Whewell equation of a plane curve is an intrinsic equation that relates the tangential angle (φ) with arclength (s). When this relation is a function, so that tangential angle is given as a function of arclength, certain properties become easy to manipulate. In particular, the derivative of the tangential angle with respect to arclength is equal to the curvature. Thus, the taking the derivative of the Whewell equation yields a Cesàro equation for the same curve.

The term is named after William Whewell, who introduced the concept in 1849, in a paper in the Cambridge Philosophical Transactions.

[edit] References

• Whewell, W. Of the Intrinsic Equation of a Curve, and its Application. Cambridge Philosophical Transactions, Vol. VIII, pp. 659-671, 1849.

• Todhunter, Isaac. William Whewell, D.D., An Account of His Writings, with Selections from His Literary and Scientific Correspondence. Vol. I. Macmillan and Co., 1876, London. Section 56: p. 317.

• Weisstein, Eric W. "Whewell Equation." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/WhewellEquation.html