The tautochrone curve is the same as the Brachistochrone curve for any given starting point.
3.
The tautochrone curve is the same as the brachistochrone curve for any given starting point.
4.
In 1696, Johann Bernoulli posed the brachistochrone problem, the solution of which is a cycloid.
5.
Instead, the brachistochrone is a half cycloid, which was only proven much later with the development of calculus.
6.
Johann Bernoulli posed the problem of the brachistochrone to the readers of " Acta Eruditorum " in June, 1696.
7.
According to Newtonian scholar Tom Whiteside, in an attempt to outdo his brother, Jakob Bernoulli created a harder version of the brachistochrone problem.
8.
He gives an erroneous solution to the brachistochrone problem, claiming to prove that the arc of the circle is the fastest descent . 16 problems with solutions are given.
9.
Each hypocycloid ( for any value of " r " ) is a brachistochrone for the gravitational potential inside a homogeneous sphere of radius " R ".
10.
The calculation of the cycloid as the brachistochrone is calculated only accounting for translational KE . I'm assuming that the cycloid still comes in first, assuming that the ball will roll on all surfaces without slipping.
