Prompt Cast
The Brachistochrone Problem and the Solution by Isaac Newton
TLDR The Brachistochrone problem, which asks what curve would allow an object to travel from point A to point B in the shortest time, was solved by Isaac Newton in a single evening. The solution is a cycloid, which is the shape you get when you roll a circle one rotation and follow a single point on the edge.
Timestamped Summary
00:00
The mathematician Johann Bernoulli posed the question of what shape would allow an object to slide down the fastest from point A to point B, which stumped many mathematicians and has interesting implications.
01:46
The Brachistochrone problem asks what curve would allow a point acted upon only by gravity to travel from point A to point B in the shortest time, and mathematicians in the 17th century struggled to find a solution.
03:03
Isaac Newton solved the Brachistochrone problem in a single evening, much faster than the other mathematicians who took over a year to solve it.
04:14
The fastest path from point A to point B is not a straight line, but rather a path that combines quick acceleration with a shorter distance, such as a steep drop followed by a horizontal run or a mathematical shape like a parabola or catenary.
05:19
The solution to the Brachistochrone problem is a cycloid, which is the shape you get when you roll a circle one rotation and follow a single point on the edge.
06:30
Snell's Law, which deals with the refraction of light, is a case of light solving the Brachistochrone problem, and there is a similar problem called the Totochrome problem that is solved by the cycloid curve.
07:43
The Totochrome problem was solved by Christian Huygens in 1659, and there are videos available online demonstrating how the Totochrome and Brachistochrome curves work.
