Entertaining video to (hopefully) increase your interest in math.
Recently, I saw this video in the “Trending” section of YouTube (3 million views). It is actually related to differential equations.
The basic question behind this is: What is the shape of the curve that will allow a ball to slide frictionlessly (under gravity) to a given end point in the shortest time? Rather surprisingly, the answer is not a straight line, even though a straight line is the shortest distance between two points.
Perhaps even more surprising is that such a curve is a tautochrone curve, where the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point
Note: Do not worry, this is not tested.
Chengyuan Wu 