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Complex Numbers and Curves

  • John Stillwell
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

There is a close connection between intersections of algebraic curves and roots of polynomial equations, going back as far as Menaechmus’ construction of \(\sqrt[3]{2}\) (a root of the equation x 3 = 2) by intersecting a parabola and a hyperbola (Section 2.4). The most direct connection, of course, occurs in the case of a polynomial curve
$$ y = p\left( x \right)$$
(1)
whose intersections with the axis y = 0 are just the real roots of the equation
$$ p\left( x \right) = 0$$
(2)
.

Keywords

Riemann Surface Branch Point Fundamental Theorem Algebraic Curf Coincident Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsMonash UniversityClaytonAustralia

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