Brachistochrone curve, faster decent than a ramp:

http://en.wikipedia.org/wiki/Brachistochrone_curve

Something I just learned. This curve connects point A, a higher point and point B, a lower point whereas an object, like a ball or a car, rolling down the ramp would take longer if it was a simple flat ramp. The Brachistochrone curve gets you from point A to point B faster than a ramp with the same A and B point.

Funny thing is, it was solved by Bernoulli in frigging 1696! using the newly developed calculus by Newton.

This is a classic problem that is often used as a means for teaching functional theory (which, I think, was unavailable to Bernouilli). I remember solving it, although I would probably have to brush up on functional theory to solve it again!

Originally posted by KazetNagorra
This is a classic problem that is often used as a means for teaching functional theory (which, I think, was unavailable to Bernouilli). I remember solving it, although I would probably have to brush up on functional theory to solve it again!

It just goes to show you how smart those dudes were.

The late great Richard Feynman cut his teeth on this type of problem using the extremal action principle in his student days. Later on he used this kind of thing as a guideline to his "sum over histories" technique in quantum field theory.

Originally posted by Paul Dirac II
The late great Richard Feynman cut his teeth on this type of problem using the extremal action principle in his student days. Later on he used this kind of thing as a guideline to his "sum over histories" technique in quantum field theory.

Wow, amazing!

Originally posted by sonhouse
Something I just learned. This curve connects point A, a higher point and point B, a lower point whereas an object, like a ball or a car, rolling down the ramp would take longer if it was a simple flat ramp. The Brachistochrone curve gets you from point A to point B faster than a ramp with the same A and B point.

Disregarding the exact shape of the curve, it is fairly obvious that a curve would be faster, as a steeper slope at the beginning would make the object accelerate faster and thus its average velocity be higher. This must be balanced against the fact that it must now travel a bit further.

Originally posted by sonhouse
It just goes to show you how smart those dudes were.

I have been watching various university physics courses and it is often amazing to me how early various parts of physics were known.
One thing I find especially interesting is how old and how far reaching Quantum Mechanics is, yet I grew up, and went through school thinking it was a very new idea with only niche applications - and never once were we taught even an overview of what it was.
With Newtonian mechanics we would be told that at higher levels of study we would come to relativity and that Newtonian mechanics was only an approximation etc.
With learning about graphs we were told that later on we could do many more things with Calculus.
But this never happened as far as I recall with quantum mechanics. It is seen by much of the public as a poorly understood side branch of science with weird effects that nobody is comfortable with.
But the reality I have come to find out in later life is that it is the foundation of much of physics, and even tells us how much of chemistry works too.