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Humbert's Theorem


The necessary and sufficient condition that an algebraic curve has an algebraic involute is that the arc length is a two-valued algebraic function of the coordinates of the extremities. Furthermore, this function is a root of a quadratic equation whose coefficients are rational functions of x and y.


See also

Algebraic Curve, Involute

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References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 195, 1959.

Referenced on Wolfram|Alpha

Humbert's Theorem

Cite this as:

Weisstein, Eric W. "Humbert's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HumbertsTheorem.html

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