Cycloids, Brachistochrones, and other Archaic Words

This didnt get a very good grade but it works to help set it up. Cycloids, Brachistochrones, and other Archaic Words Introduction: Everyone with a decent math background knows that a straight line is the shortest distance between two points. Intuitively, many would think that it would also be the path taken that took the shortest amount of time. We will show that the time that it takes to traverse cycloidal and elliptic path is …

…we can use that fact to our advantage. The equation represents the velocity between two points due to gravity. After we have found the velocity we can apply the time integral. . If you do a unit analysis on this integral it makes sense, m stands for meters, and s stands for seconds. The first derivative of a function is the velocity of that function. Time of the line segment: Time of cycloid: Time of ellipse: