Yes. I think this is the sort of toy John Bernoulli made for his sons.

The question is? shortest travel time?

- Cuchulainn
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Yes. I think this is the sort of toy John Bernoulli made for his sons.

The question is? shortest travel time?

The question is? shortest travel time?

Yes, the question is: why is the wavy one faster then the flat one?

And this one: why doesn't the bottom fall?

- Cuchulainn
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Yes, the question is: why is the wavy one faster then the flat one?

The wavy one is not always faster everywhere; but the total transit time is less. If you know y' then you can compute the integral by finite difference etc.

If want to get from start to finish ASAP, then minimising the integral will be a

Last edited by Cuchulainn on July 23rd, 2017, 4:45 pm, edited 2 times in total.

- Cuchulainn
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A family that plays together, stays together.And this one: why doesn't the bottom fall?

My guess is it does not have enough kinetic energy. You can put the motion in Lagrange's equation and solve.

I've read more "intuitive" explanations instead of the exact equations you've mentioned! I'll wait a bit with disclosing the explanations I found, ok?

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Maybe for that annual Dutch quiz 2017?

Mrs. Cuchulainn got the first one right (without any maths!)

Mrs. Cuchulainn got the first one right (without any maths!)

- Cuchulainn
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What is the shape of a bull's hide?

"The Kingdom you see is Carthage, the Tyrians, the town of Agenor;

But the country around is Libya, no folk to meet in war.

Dido, who left the city of Tyre to escape her brother,

Rules here--a long and labyrinthine tale of wrong

Is hers, but I will touch on its salient points in order....Dido, in great disquiet, organised her friends for escape.

They met together, all those who harshly hated the tyrant

Or keenly feared him: they seized some ships which chanced to be ready...

They came to this spot, where to-day you can behold the mighty

Battlements and the rising citadel of New Carthage,

And purchased a site, which was named 'Bull's Hide' after the bargain

**By which they should get as much land as they could enclose with a bull's hide."**

"The Kingdom you see is Carthage, the Tyrians, the town of Agenor;

But the country around is Libya, no folk to meet in war.

Dido, who left the city of Tyre to escape her brother,

Rules here--a long and labyrinthine tale of wrong

Is hers, but I will touch on its salient points in order....Dido, in great disquiet, organised her friends for escape.

They met together, all those who harshly hated the tyrant

Or keenly feared him: they seized some ships which chanced to be ready...

They came to this spot, where to-day you can behold the mighty

Battlements and the rising citadel of New Carthage,

And purchased a site, which was named 'Bull's Hide' after the bargain

- Traden4Alpha
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Initially, the bottom of the spring is in equilibrium between the downward pull of gravity and upward pull of the spring (and the distribution of gravity. When the top is released, the top is double-accelerated by BOTH gravity and the spring force but the bottom remains in equilibrium with gravity pulling down and the residual per-unit-length spring force pulling up.

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The ball track one may be caused by the m*g*h potential energy differences in the two tracks in which the wavy track has deeper valleys that induce the ball to "proportionally"* higher velocities and yet the distances are not proportionally longer.

* "proportionally" in an O(mgh) = O(mv^2) sense and reflecting the relative effects of linear and rotational inertia of the rolling ball.

* "proportionally" in an O(mgh) = O(mv^2) sense and reflecting the relative effects of linear and rotational inertia of the rolling ball.

Clearer with a half pipe, I think.

If this half pipe was very shallow, it's perhaps obvious the time to reach the bottom would be longer. By symmetry, the time to reach all the way across would be twice that time.

If this half pipe was very shallow, it's perhaps obvious the time to reach the bottom would be longer. By symmetry, the time to reach all the way across would be twice that time.

- Cuchulainn
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BTW, the cycloid is also the geodesic for the Heston model asymptotics: Gulisashvili &

Laurence

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I browsed through the article couple times but was unable to see the goal, neither in the Abstract nor the Conclusion. It's a bit high-falutin' maths and excellent maths.BTW, the cycloid is also the geodesic for the Heston model asymptotics: Gulisashvili &

Laurence

Does the paper relate to a minimisation of a functional?

GZIP: On