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Klein's Equation


If a real algebraic curve has no singularities except nodes and cusps, bitangents, and inflection points, then

 n+2tau_2^'+iota^'=m+2delta_2^'+kappa^',

where n is the order, tau^' is the number of conjugate tangents, iota^' is the number of real inflections, m is the class, delta^' is the number of real conjugate points, and kappa^' is the number of real cusps. This is also called Klein's theorem.


See also

Plücker's Equation

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References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 114, 1959.

Referenced on Wolfram|Alpha

Klein's Equation

Cite this as:

Weisstein, Eric W. "Klein's Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KleinsEquation.html

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