Is a straight line the fastest way between two points?

[panyamnyenyekevu]

Depends!

6C8C7633-41A2-4D5E-A1C1-A4AB9759732E.gif (27.1 KiB) Viewed 436 times

[Corinnebelle]

Which two points are we talking about?

[Davey944676]

I'm not sure what it's supposed to represent...is it some sort of perspective thing?

Whatever it is, that little animation is somehow rather soothing and satisfying to watch.....

[panyamnyenyekevu]

I'm not sure what it's supposed to represent...is it some sort of perspective thing?

Whatever it is, that little animation is somehow rather soothing and satisfying to watch.....

[mathemajician]

A (somewhat related) cartoon I've always loved.

[Davey944676]

Thanks pany and mathy, but my browser settings are a bit blocking many Twitter et al things, and it's too late and complicated right now for me to rset them!

[panyamnyenyekevu]

Thanks pany and mathy, but my browser settings are a bit blocking many Twitter et al things, and it's too late and complicated right now for me to rset them!

Text of tweet by @Rainmaker1973 (<—- twitter handle)

One property of the lemniscate of Bernoulli is that a ball rolling down an arc of the lemniscate under the influence of gravity, will take the same time to traverse it as a ball rolling down a straight line segment connecting the endpoints of the arc buff.ly/2FU0i5c

[Corinnebelle]

Now I get it, maybe! Basically the influence of centrifugal force combined with gravity has a greater pull than gravity alone. Is there some sort of triangle effect in play here?

I didn't understand gravity was at play in the gif, I notice that dot that goes round slows down as it returns to center. Why is that?

[panyamnyenyekevu]

Now I get it, maybe! Basically the influence of centrifugal force combined with gravity has a greater pull than gravity alone. Is there some sort of triangle effect in play here?

I didn't understand gravity was at play in the gif, I notice that dot that goes round slows down as it returns to center. Why is that?

“Triangle effect?” What’s that?

The dot slows down because it’s going uphill.

I don’t understand the math and physics well enough to understand it myself, but it seems deeply intuitive and meaningful and it’s related to the tautochrone or isochronous curve and the brachistochrone.

https://en.m.wikipedia.org/wiki/Tautochrone_curve

https://en.m.wikipedia.org/wiki/Brachistochrone_curve

[mention]Davey944676[/mention] [mention]Nineko[/mention] [mention]duome[/mention] [mention]mathemajician[/mention]

[Corinnebelle]

Ok, so this is a special curve. I was wondering if the ball goes faster depending on the angle of the curve. [That's what I meant by triangular effect, depending on the curve on a graph. Not very smart I know.] That is a very interesting video. The isochronous curve is like what happens when you stretch out a circle. So what is the secret that makes the ball go faster on a curve than straight?