Geometry of Cubic Polynomials
Drag the vertices to see how any three real numbers, not all equal, are the projections of the vertices of an equilateral triangle in the plane. For a cubic polynomial with three real roots (not all equal), the inscribed circle of the equilateral triangle that projects onto those roots itself projects to an interval with endpoints equal to the roots of , the derivative of
 S. Northshield, "Geometry of Cubic Polynomials," Mathematics Magazine, 86, 2013 pp. 136–143.
"Geometry of Cubic Polynomials"
Wolfram Demonstrations Project
Published: September 30 2013