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Plane Curves with Pseudo-Rhamphoid Cusps


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1 University of California, United States
     

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A necessary condition that the parametric equations

x = f(T), y = g(T)                            (1)

represent the plane algebraic curve U(x, y) = 0 is that U [f(T), g(T)] = 0 in the parameter T. This condition merely states that the points given by the equations (1) are points of the curve U(x, y) = 0, and does not imply that to every point of the curve there corresponds a value of T.


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  • Plane Curves with Pseudo-Rhamphoid Cusps

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Authors

Clifford Bell
University of California, United States

Abstract


A necessary condition that the parametric equations

x = f(T), y = g(T)                            (1)

represent the plane algebraic curve U(x, y) = 0 is that U [f(T), g(T)] = 0 in the parameter T. This condition merely states that the points given by the equations (1) are points of the curve U(x, y) = 0, and does not imply that to every point of the curve there corresponds a value of T.