Center of an Equilateral Triangle Circumscribing a Given Parabola
Center of an Equilateral Triangle Circumscribing a Given Parabola
If an equilateral triangle circumscribes a parabola, that is, its sides (extended if necessary) are tangent to the parabola, then its center moves along a straight line, which is none other than the parabola's directrix. To prove this was a question in the oral examination of the Ecole Polytechnique in 1928.