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Werner_E
Werner_EAnswer
25-Diamond I
December 25, 2020

I wasn't aware of this new exact solution to the problem - thanks for bringing this to our attention.

 

Obviously we cannot expect Mathcad to give us the "exact" solution, but it sure is good enough for an approximation:

Werner_E_1-1608909203500.png

 

By the way, the wiki entry for the goat problem has already been supplemented by Ingo Ullisch's closed form solution -> https://en.wikipedia.org/wiki/Goat_problem#Closed-form_solution

 

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9 replies

Werner_E
Werner_E25-Diamond IAnswer
25-Diamond I
December 25, 2020

I wasn't aware of this new exact solution to the problem - thanks for bringing this to our attention.

 

Obviously we cannot expect Mathcad to give us the "exact" solution, but it sure is good enough for an approximation:

Werner_E_1-1608909203500.png

 

By the way, the wiki entry for the goat problem has already been supplemented by Ingo Ullisch's closed form solution -> https://en.wikipedia.org/wiki/Goat_problem#Closed-form_solution

 

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    Fred_Kohlhepp23-Emerald IAuthor
    23-Emerald I
    December 25, 2020

    Okay, where's my mistake?

    Fred_Kohlhepp_0-1608916916113.png

     

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    Werner_E
    Werner_E25-Diamond I
    25-Diamond I
    December 25, 2020
    @Fred_Kohlhepp wrote:

    Okay, where's my mistake?

    It here, as the area should be just half of the area of the fenced circle.

    Werner_E_0-1608921965487.png

     

    BTW, your function A.g(r) only returns a correct result for the area between the two circles if r<=sqrt(2)*R.f.

    If the goat circle intersects the fence circle above the x-axis, you get wrong results.

     

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      ValeryOchkov24-Ruby IV
      24-Ruby IV
      December 25, 2020

      See the attach and

      https://community.ptc.com/t5/PTC-Mathcad/NEW-CONSTANT-in-math/m-p/352621

       

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      Werner_E
      Werner_E25-Diamond I
      25-Diamond I
      December 25, 2020

      Nice idea to make the area ratio selectable.
      But the link in the thread you point to is dead and the plot in the attached worksheet fails. I guess the file is from the times of the Mathcad Application Server and you added units. If you do so, you would also have to change the plot by providing a range for l and unfixing the upper limit of the y-axis:

      Werner_E_0-1608923377012.png

      Unfortunately the file does not show the derivation of the formula using the capabilities of Mathcad.

       

       

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