A parabolic segment is the region bounded by a parabola and line. To find[br]the area of a parabolic segment, Archimedes considers a certain inscribed[br]triangle. The base of this triangle is the given chord of the parabola, and the[br]third vertex is the point on the parabola such that the tangent to the[br]parabola at that point is parallel to the chord.[br]Move points A and B and look at the values of the areas.[br]The blue triangle area is always 1/8 of the red one and the green triangle area is 1/8 of the blue one!