Plücker's Equations
Relationships between the number of Singularities of plane algebraic curves.Given a Plane Curve,
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
 | |  | (4) |
where
is the Class, 
the Order, 
the number ofNodes, 
the number of Cusps, 
the number ofStationary Tangents (Inflection Points), and 
the number ofBitangents. Only three of these equations are Linearly Independent.See also Algebraic Curve, Bioche's Theorem, Bitangent, Cusp, Genus (Surface), Inflection Point, Klein's Equation,Node (Algebraic Curve), Stationary Tangent
References
Boyer, C. B. A History of Mathematics. New York: Wiley, pp. 581-582, 1968. Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 99-118, 1959.
- Kummer's Series Transformation
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