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 EquationExplore with Wolfram|Alpha
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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 EquationCite this as:
Weisstein, Eric W. "Klein's Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KleinsEquation.html