Tolstoy-Ellipse

[ValeryOchkov]

Cassini oval - Wikipedia

My attempt to find a, c and x1 is in attach - MC15 and Prime 6

Help please

[Werner_E · Accepted solution]

How about adding a scaling factor?

[ValeryOchkov]

New math constant?

a/c=1.4142...

c/a=0.70711...

[Werner_E]

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@ValeryOchkov wrote:

New math constant?

a/c=1.4142...

c/a=0.70711...

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No, not new. Just sqrt(2) 🙂

y''(0)=0 is equivalent with a = c* sqrt(2)

You could use this right from the start in your equation.

[Werner_E]

Sorry, the addition of the scaling factor was rather nonsense. Scaling the parameters a and c do the same job, so f is not necessary at all. I guess that getting rid of your variable x1 did the job.

So a shorter solution is this:

[Werner_E]

And here is an even shorter approach which uses, that for the curve you are looking for we have a=c*sqrt(2)

[Werner_E]

This seems to be so far the shortest solution.

Using no symbolic and no solve block

[ValeryOchkov]

[Werner_E]

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@ValeryOchkov wrote:

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???????

[ValeryOchkov]

Tolstoy oval

[Werner_E]

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@ValeryOchkov wrote:

Tolstoy oval

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Yes, I was pretty sure that you still were working on the "Tolstoy oval" you mentioned here https://community.ptc.com/t5/PTC-Mathcad/Leo-Tolstoy-and-Mathcad/m-p/707187#M193887

But now you have to give a concrete mechanical construction method, how one could have drawn this Cassini oval back then. Something similar to the two pegs and the rope with which you can create an ordinary ellipse. I am very curious already  😉

[ValeryOchkov]

There is such a smart rope - you intercept it into two parts, and the product of the lengths of these parts does not change! a^2!

[Werner_E]

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@ValeryOchkov wrote:

There is such a smart rope - you intercept it into two parts, and the product of the lengths of these parts does not change! a^2!

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Too bad that the knowledge of this special type of rope has been forgotten over time and they are no longer made these days 🙂

[ValeryOchkov]

I have a little

[ValeryOchkov]