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|dw:1347894497129:dw|

geowotsit?

assume both h and w are not zero.

|dw:1347894819011:dw|

it's a pretty famous problem ...

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

yep ... this is brachistochrome problem.

cycloid is a shape made my rolling circle.
http://en.wikipedia.org/wiki/Cycloid

I was thinking geodesic at first, shortest distance....

i did this with calculus of variation. haven't done this with purely calculus.

What about when h=w and h and approaches infinity

h and w*

take a circle with zero radius, you will get a straight line.

* if w = 0 ...

|dw:1347895370580:dw|

I got that cycloid part........

What if h and w approaches infinity.....

It will never get to the bottom and you will never know..:-)

Then I think this should work:|dw:1347895555863:dw|

yep ... this is a physics problem actually.

Will it still be that cycloid

yep .. it should be cycloid ... make by a huge circle.

OMG! This math stuff is out my level

Didnt get why cycloid........ I just know we need to maximise the accleration

or sphere, perhaps..

I mean why cycloid is the answer to @experimentX question

It will only increase the length

When you solve the problem, that's what comes out, a deeper meaning, you mean?

oh

trust me ... things aren't that intuitive.

Ok..... I trust u. @experimentX

When did u learnt these stuff. @experimentX

i was wondering if anyone could solve it using purely calculus. I haven't tried it yet.

At university

I will think on this problem.... see If I can get to the solution

told you i'm old guy