Leo Tolstoy and Mathcad

[ValeryOchkov]

"The race course was a large three-mile ring of the form of an ellipse...".

Anna Karenina, by Leo Tolstoy Translated by Constance Garnett

In Russian text not three-mile, but 4 versta (верста). Versta = 500 Sagen (сажень), Sagen = 7 feets.

The problem.

The workers marked this racetrack like that. They took a rope and tied it with both ends to two pegs driven into the ground and spaced one versta (see above) from each other. Then they pulled this rope and drew an ellipse. How long was this rope? What is the canonic formula of this ellipse?
Who will give the best solution? 

[Werner_E]

Guess you know that you can't expect a symbolic solution, do you?

Quite a long rope for the time

[ValeryOchkov]

Thanks, Werner!

One more from Anna Karenina

"- Самолюбия, - сказал Левин, задетый за живое словами брата, - я не понимаю. Когда бы в университете мне сказали, что другие понимают интегральное вычисление, а я не понимаю, - тут самолюбие."

“Self-respect!” said Levin, stung to the quick by his brother’s words; “I don’t understand. If they’d told me at college that other people understood the integral calculus, and I didn’t, then pride would have come in.

Sorry, I know more nice solution.

PS

One interesting article about math and not Leo Tolstoy but Fedor Dostoyevsky

Dostoyevsky as mathematician (part II) | SpringerLink

[AlanStevens]

Here's a more long-winded approach than Werner's. It produces a slightly different result.

 

[AlanStevens]

Hmm.  I tried to post another solution, but had an email saying it was rejected by a moderator.  Any idea why? (It contained a jpg image).

I'll try just attaching the (M15) file instead.

My approach was more long-winded than Werner's and produced a slightly different result.

Alan

[Werner_E]

Are you sure about the formula for the arc length?

Shouldn't it be rather that way:

The difference to my result is now about 1.7*10^-6 % which seems acceptable to me.

Because the Integral uses the derivative of a solve block function, calculation is very slow and a lot of numeric round-offs may sum up.

According your post being rejected by a mod. This really should not happen and is quite strange - especially given the fact, that you sure have built a reputation for yourself as a serious and very valuable forum participant over many years. I also thought that only the postings of new members would be under moderation anyway.

Maybe @Jaime_Lee  can shed some light on this.

P.S.: Its nice to see you being around here again!

[AlanStevens]

Thanks Werner, you might be right about the distance, I did it rather quickly, without too much thought - I'll think on it more deeply!

I still look at the site from time to time, but it seems there are more and more PRIME related questions.  Since I don't have PRIME I take little interest in them!

Alan

[Werner_E]

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@AlanStevens wrote:

Thanks Werner, you might be right about the distance, I did it rather quickly, without too much thought - I'll think on it more deeply!

I still look at the site from time to time, but it seems there are more and more PRIME related questions.  Since I don't have PRIME I take little interest in them!

Alan

---

Yes, Prime sucks and I usually fire it up only to answer questions here in the forum. As long as we have access to real Mathcad, I see no need to actually use Prime, even though Luc had provided a real interesting collection of work-arounds to duplicate a lot of premium functions in Prime Express. You sure know that you can install Prime in parallel with real Mathcad and that you can still use Prime after its evaluation time in its limited "Express" mode.

[AlanStevens]

Hi Werner, 

Yes I do know PRIME can be installed alongside M15, and that it becomes the Express version after 30 days or so.  However, I'm simply not motivated enough to do that!  I'll just stick with M15.

Alan

[ValeryOchkov]

My solution

[ValeryOchkov]

But it was not an ellipse - if was an oval or 2 lines + 2 arcs.

One frame from the movie 

[Werner_E]

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@ValeryOchkov wrote:

But it was not an ellipse - if was an oval or 2 lines + 2 arcs.

---

Are you saying that you lied by writing " Then they pulled this rope and drew an ellipse."? 🙂

[ValeryOchkov]

Sagen = 7 feets

The woman measures, the man counts

[Jaime_Lee]

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@AlanStevens wrote:

Hmm.  I tried to post another solution, but had an email saying it was rejected by a moderator.  Any idea why? (It contained a jpg image).

I'll try just attaching the (M15) file instead.

My approach was more long-winded than Werner's and produced a slightly different result.

Alan

---

Hi, @AlanStevens   Your solution you are trying to provide got caught in the "automatic" SPAM queue (based on the longer string of characters (formula) in your message. The Spam queue is typically reviewed and monitored by moderator team.  I am sorry no one got to it fast enough because it definitely wasn't quick enough.  Would you be so kind to send the email message you received to community@ptc.com.  I should probably make adjustments to the templated information.  Also, @Werner_E is correct  when he says "This really should not happen and is quite strange - especially given the fact, that you sure have built a reputation for yourself as a serious and very valuable forum participant over many years."    We appreciate your contributions and would love for you to continue to share your expertise on the PTC Community!

[AlanStevens]

@ Jaimee_Lee  Thanks for the explanation.

I'm afraid I can't send the email as I deleted it immediately (from both my inbox and trash can)! 

I see that my mistaken calculation now appears several times!!!

Alan

[Jaime_Lee]

@AlanStevens   No worries!  I can dig into the platform templates and try to find it 🙂  Also, if you are uncomfortable with your post (now visible) AND in the attachment on the second post, we can delete it instead of releasing it from "spam jail" for you.  It kind of helps the flow of conversation when people don't have to click on the attachment to see it, but just use "Notify Moderator" on the post you would like to suggest the Moderator delete.

[ValeryOchkov]

Hi @Jaime_Lee 

did you read the Anna Karenina novel by Лев Толстой?

[Jaime_Lee]

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@ValeryOchkov wrote:

Hi @Jaime_Lee 

did you read the Anna Karenina novell by Лев Толстой?

---

Can't say I have!  Should we start up some book reviews on the PTCooler?

https://community.ptc.com/t5/PTCooler-OffTopic/bd-p/ThePTCoolerDiscussions

if @Dale_Rosema  (who I have nominated to be the President or the King of the Cooler agrees) 😉 I will move this post over and we can start chatting about this book!

[ValeryOchkov]

You are a happy person - you have not read the Anna Karenina novell yet!

[Jaime_Lee]

Just looked it up on Wikipedia. 800 pages! Sounds like a pretty involved plot!

https://en.wikipedia.org/wiki/Anna_Karenina

I think for now if we were to start any "Book Review" conversations on the PTCooler maybe we should stick with Engineering related topics 🙂

[ValeryOchkov]

[ValeryOchkov]

Mathcad and Jules Verne - Wikipedia

Computation | Free Full-Text | Symbolic Computation to Solving an Irrational Equation on Based Symmetric Polynomials Method | HTML (mdpi.com)

[ValeryOchkov]

I vave a lot of same problems here

2⁵ Problems for STEM Education - 1st Edition - Valery Ochkov - Rout (routledge.com)

Examples

[Fred_Kohlhepp]

And, if you're stuck with Express:

[ValeryOchkov · Accepted solution]

For Express- not 3 but one equation

[ValeryOchkov]

in Russian

1 верста

2 версты (two of versta)

3 версты

4 версты

5 верст

6 верст

7 верст

8 верст

9 верст

...

21 верста

etc

[ValeryOchkov]

Leo Tolstoy. One picture by Valery

(no solution without animation!)

[AlanStevens]

Thought I'd have another go (and also see if I can upload images yet!):

Alan

[ValeryOchkov]

Solution of new problem - not S=1верста, but Gold Ellipe!

Red - a gold ellipse, Blue S=1 versta

[ValeryOchkov]

https://en.wikipedia.org/wiki/Silver_ratio