Brachistochrone problem

Rating: 8/10 (20 July 2004)

This post is not supposed to be interesting to everyone, OK? I'm just sharing a detail in the movie I liked a lot.
When Peter and Dr. Otto were talking about sleeping before the great day, and Dr. Otto gave examples such as Edison, Marconi and Beethoven, Peter said something like that "Did Bernoulli sleep before finding the curve of fastest descent?"
This curve of fastest descent is the brachistochrone, that is, the curve joining two given points along which a particle falling from rest accelerated only by gravity travels in the least time. It can also be seen as what shape should a roller-coaster through two points have in order to get to the bottom in the least time possible.
This is the major theme in my Masters thesis, on History of Mathematics, and that is why I find this phrase interesting.
It was Johann Bernoulli the first one to solve the brachistochrone, although it was first stated by Galileo Galilei. Bernoulli then challenged the mathematicians of his time to solve the problem, an it is said that when Isaac Newton received the challenge, in spite of being tired after a day of work, he didn't sleep until he found the solution, which is an arc of an inverted cycloid.
If you want to know more about this (which I doubt!), just type brachistochrone in yahoo, google,...
Crente (that is, "believer" in Portuguese)