> Another interesting thing about a cycloid-shaped ramp is that no matter how high up the ramp you let a ball go from, it will take the same amount of time to get from that point to the bottom.
>
> ^v^:)^v^
> FB

That makes sense, I guess. But I keep sitting here thinking about variations in temperature, air pressure, and friction.

I had a physics teacher once who asked how big a mirror had to be for you to see your whole length. He insisted that it would have to be about half as tall as you are. But I asked him if a smaller mirror wouldn't do, provided it was above you. He got very quiet for a few minutes.

I think I must be making a point that I don't always look at a problem the way most people do.
Howard