The ElonU Tangential’s student group solved the AMM problem 12476 which states: Let be one arch of the elliptic cycloid generated by the ellipse . That is, let be the curve traced by the vertex at the origin as the ellipse rolls without slipping along the -axis for one revolution. What is the area under and above the -axis?
Our solution uses a clever change of perspective letting a tangent line roll around the ellipse, instead of the ellipse roll along the -axis. The desired area turns out to be a surprisingly simple number.