56. Area of a Parabola - Archimedes

Archimedes gave a method for calculating the area of a given parabola section.

Archimedes' solution is a nice alternative to integration. GGB does not recognize that my parabola is a function. Integral[] gives an error. Polynomial[A,O,C] works but needs three (or four) points on the curve, which is given by Focus and Directrix (0 points on the curve). If the axis is not vertical, the integral may need to be done in pieces. Archimedes' approach is the same regardless of orientation, quick and easy to do in GGB. We can even use it to draw a parabola from scratch. A nice alternative that holds its own in the computer age.