Descartes's Method of Evaluating the Principal Cube Root

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Descartes used the parabola with the equation and the circle with center passing through to construct the real or principal cube root . Every real number greater than zero has one real cube root and a pair of complex conjugate cube roots.

Contributed by: Izidor Hafner (August 2017)
Open content licensed under CC BY-NC-SA



This Demonstration is based on [1, p. 51, p. 165].

If and , then or . Namely, substituting the first equation into the second and simplifying, we get .


[1] G. E. Martin, Geometric Constructions, New York: Springer, 1998.

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