Omar Khayyam's geometric solution of a cubic equation
Omar Khayyam's method to solve the cubic equation . Khayyam showed that the solution could be found from the intersection point of a parabola with a semi-circle. By varying the scale of the parabola and the diameter of the circle you can solve the cubic equation for any positive value of and .
This diagram solves the cubic equation . The value of is represented by the area of the square OABC. The circle's diameter OD is . The solution of the cubic equation is given by the length OQ. You can vary by dragging the point A left or right, and you can change the diameter by dragging point D. See if you can find the solution of and of .