Descartes's Method of Evaluating the Principal Cube Root

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.


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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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