# Omar Khayyam's approach to solving certain cubic equations

Omar Khayyam (al-Khayyami, 1048-1131), mathematician, philosopher and poet laid down the gauntlet for the algebraic solution of cubic equations. Here we see how he tackled $x^3+cx=d$, where $c$ and $d$ are given positive constants. To solve the given cubic equation using Khayyam's method, let |AB| = $\sqrt{c}$ and |BC| = $\frac{d}{c}$. Construct the semi-circle on diameter BC and the parabola $y=\frac{x^2}{\sqrt{c}}$, as shown, intersecting at D. Complete the rectangle BEDZ. Then $x=|BE|$ satisfies the given cubic.

Explore the problem by adjusting the sliders. Investigate why Khayyam's method works. Compare his method with those of other mathematicians, such as Cardano. Reference: [i]A History of Mathematics - an introduction [/i]by VG Katz (1993). Find out more about Khayyam on the web.