Date: 3/04/2022 14:08:14
From: The Rev Dodgson
ID: 1868421
Subject: The Challenge of the Brachistochrone

I thought this was QI:

The Challenge of the Brachistochrone

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Date: 3/04/2022 14:10:19
From: sibeen
ID: 1868423
Subject: re: The Challenge of the Brachistochrone

https://www.youtube.com/watch?v=eBc827pwKf0&ab_channel=CuriosityShow

The Curiosity show did this back in the 70s.

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Date: 3/04/2022 14:12:10
From: The Rev Dodgson
ID: 1868425
Subject: re: The Challenge of the Brachistochrone

sibeen said:


https://www.youtube.com/watch?v=eBc827pwKf0&ab_channel=CuriosityShow

The Curiosity show did this back in the 70s.

I’m impressed with your powers of memory :)

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Date: 3/04/2022 14:14:07
From: sibeen
ID: 1868427
Subject: re: The Challenge of the Brachistochrone

The Rev Dodgson said:


sibeen said:

https://www.youtube.com/watch?v=eBc827pwKf0&ab_channel=CuriosityShow

The Curiosity show did this back in the 70s.

I’m impressed with your powers of memory :)

I may, just may, have seen it since :)

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Date: 3/04/2022 14:26:32
From: mollwollfumble
ID: 1868433
Subject: re: The Challenge of the Brachistochrone

The Rev Dodgson said:


I thought this was QI:

The Challenge of the Brachistochrone

Reminds me of the cycloid.

IIRC The mathematical proof that the cycloid is the fastest route from A to B under the influence of gravity is a really beautiful thing. Again IIRC, it was an early application of the calculus of variations, and not something I could have solved myself.

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Date: 3/04/2022 14:34:22
From: The Rev Dodgson
ID: 1868437
Subject: re: The Challenge of the Brachistochrone

mollwollfumble said:


The Rev Dodgson said:

I thought this was QI:

The Challenge of the Brachistochrone

Reminds me of the cycloid.

IIRC The mathematical proof that the cycloid is the fastest route from A to B under the influence of gravity is a really beautiful thing. Again IIRC, it was an early application of the calculus of variations, and not something I could have solved myself.

It’s another name for the cycloid.

It seems Newton solved it with his very basic calculus, so I expect you could solve it, if you hit on the right approach.

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Date: 3/04/2022 14:37:56
From: The Rev Dodgson
ID: 1868439
Subject: re: The Challenge of the Brachistochrone

The Rev Dodgson said:


mollwollfumble said:

The Rev Dodgson said:

I thought this was QI:

The Challenge of the Brachistochrone

Reminds me of the cycloid.

IIRC The mathematical proof that the cycloid is the fastest route from A to B under the influence of gravity is a really beautiful thing. Again IIRC, it was an early application of the calculus of variations, and not something I could have solved myself.

It’s another name for the cycloid.

It seems Newton solved it with his very basic calculus, so I expect you could solve it, if you hit on the right approach.

I’ll add that I have long been interested in the calculus of variations, but every book I have seen on the subject has been too mathematical for my engineering brain, so they tend to lose me after about 1 1/2 pages.

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Date: 3/04/2022 15:06:04
From: btm
ID: 1868447
Subject: re: The Challenge of the Brachistochrone

The Rev Dodgson said:


I’ll add that I have long been interested in the calculus of variations, but every book I have seen on the subject has been too mathematical for my engineering brain, so they tend to lose me after about 1 1/2 pages.

See if you can find a book called Foundations of Applied Mathematics by Michael D. Greenberg. Greenberg’s coverage of the calculus of variations is the best I’ve found. The brachistochrone problem is included as an exercise.

The brachistochrone is also known as a tautochrone. Why?

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Date: 3/04/2022 15:07:55
From: The Rev Dodgson
ID: 1868448
Subject: re: The Challenge of the Brachistochrone

btm said:


The Rev Dodgson said:

I’ll add that I have long been interested in the calculus of variations, but every book I have seen on the subject has been too mathematical for my engineering brain, so they tend to lose me after about 1 1/2 pages.

See if you can find a book called Foundations of Applied Mathematics by Michael D. Greenberg. Greenberg’s coverage of the calculus of variations is the best I’ve found. The brachistochrone problem is included as an exercise.

The brachistochrone is also known as a tautochrone. Why?

Thanks btm, I’ll have a look.

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Date: 3/04/2022 15:13:35
From: The Rev Dodgson
ID: 1868451
Subject: re: The Challenge of the Brachistochrone

The Rev Dodgson said:


btm said:

The Rev Dodgson said:

I’ll add that I have long been interested in the calculus of variations, but every book I have seen on the subject has been too mathematical for my engineering brain, so they tend to lose me after about 1 1/2 pages.

See if you can find a book called Foundations of Applied Mathematics by Michael D. Greenberg. Greenberg’s coverage of the calculus of variations is the best I’ve found. The brachistochrone problem is included as an exercise.

The brachistochrone is also known as a tautochrone. Why?

Thanks btm, I’ll have a look.

It;s available for free download from somewhere called booksmain.club,

Anyone know if they are safe to sign up to?

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Date: 3/04/2022 15:28:39
From: btm
ID: 1868455
Subject: re: The Challenge of the Brachistochrone

The Rev Dodgson said:


The Rev Dodgson said:

btm said:

See if you can find a book called Foundations of Applied Mathematics by Michael D. Greenberg. Greenberg’s coverage of the calculus of variations is the best I’ve found. The brachistochrone problem is included as an exercise.

The brachistochrone is also known as a tautochrone. Why?

Thanks btm, I’ll have a look.

It;s available for free download from somewhere called booksmain.club,

Anyone know if they are safe to sign up to?

According to https://www.scamadviser.com/check-website/booksmain.club, it has “a low trust score” and may be a scam; according to Norton (of antimalware fame) it’s a “known dangerous webpage”.

I’d avoid it.

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Date: 3/04/2022 16:00:18
From: The Rev Dodgson
ID: 1868469
Subject: re: The Challenge of the Brachistochrone

btm said:


The Rev Dodgson said:

The Rev Dodgson said:

Thanks btm, I’ll have a look.

It;s available for free download from somewhere called booksmain.club,

Anyone know if they are safe to sign up to?

According to https://www.scamadviser.com/check-website/booksmain.club, it has “a low trust score” and may be a scam; according to Norton (of antimalware fame) it’s a “known dangerous webpage”.

I’d avoid it.

Since they are supplying for “free” something Amazon charge about $35 for, that’s probably good advice :)

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Date: 3/04/2022 16:05:44
From: SCIENCE
ID: 1868474
Subject: re: The Challenge of the Brachistochrone

The Rev Dodgson said:


btm said:

The Rev Dodgson said:

It;s available for free download from somewhere called booksmain.club,

Anyone know if they are safe to sign up to?

According to https://www.scamadviser.com/check-website/booksmain.club, it has “a low trust score” and may be a scam; according to Norton (of antimalware fame) it’s a “known dangerous webpage”.

I’d avoid it.

Since they are supplying for “free” something Amazon charge about $35 for, that’s probably good advice :)

how’s sci hub been going for you all lately

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Date: 3/04/2022 19:39:11
From: mollwollfumble
ID: 1868545
Subject: re: The Challenge of the Brachistochrone

> See if you can find a book called Foundations of Applied Mathematics by Michael D. Greenberg. Greenberg’s coverage of the calculus of variations is the best I’ve found. The brachistochrone problem is included as an exercise.

Noted. Published 2013.
Website “https://www.perlego.com/book/113158/foundations-of-applied-mathematics-pdf” says free trial available.

I did understand calculus of variations many years ago, but it’s not something that I ever needed to know for my work with CSIRO.

IIRC, calculus of variations can be used in truss design, and that might be an easy way to learn it.

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Date: 14/04/2022 12:40:44
From: mollwollfumble
ID: 1872623
Subject: re: The Challenge of the Brachistochrone

mollwollfumble said:


> See if you can find a book called Foundations of Applied Mathematics by Michael D. Greenberg. Greenberg’s coverage of the calculus of variations is the best I’ve found. The brachistochrone problem is included as an exercise.

Noted. Published 2013.
Website “https://www.perlego.com/book/113158/foundations-of-applied-mathematics-pdf” says free trial available.

I did understand calculus of variations many years ago, but it’s not something that I ever needed to know for my work with CSIRO.

IIRC, calculus of variations can be used in truss design, and that might be an easy way to learn it.

Oh, here’s the thread.

Looks like I need calculus of variations to minimise the volume of excavation needed to stop flooding in Gympie. :-(

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