Solving a Cubic via the Trisection of an Angle

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This Demonstration shows a geometric solution to the equation , where and are real in the case where the equation has three distinct real roots (i.e. has a positive discriminant). It is based on Viète's trigonometric solution of the cubic that constructs and trisects a particular angle associated with the given cubic equation.

Contributed by: Christopher Moretti (October 2012)
Open content licensed under CC BY-NC-SA



For a detailed discussion of the trigonometric solution to the cubic, see [1] or [2].


[1] G. E. Martin, Geometric Constructions, New York: Springer–Verlag, 1998 p. 132–133.

[2] D. A. Cox, Galois Theory, New York: John Wiley & Sons, 2004 p. 18–19.

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