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Klein's Equation

If a Real curve has no singularities except nodes and Cusps, Bitangents, and Inflection Points, then


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


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

© 1996-9 Eric W. Weisstein