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DaveMartin16-Pearl
16-Pearl
May 3, 2022

Mathcad Community Challenge May 2022 - An Isoperimetric Geometry Problem

  • May 3, 2022
  • 9 replies
  • 15323 views

The first two challenges were biased towards mechanical engineering. May’s challenge pertains to geometry.

Create a worksheet in which you calculate (1) the diameter of a circle and (2) the length of a side of a square that yields the minimum combined area for a combined perimeter of 1 meter.

This is an optimization problem. What tools within Mathcad can provide you with a result?

Optional: How can you depict the results? Can you use a 2D plot or Chart Component to visualize the answer?
Find the Mathcad Community Challenge Guidelines here!

 

    9 replies

    T
    21-Topaz II
    terryhendicott21-Topaz II
    21-Topaz II
    May 4, 2022

    Hi,

    I'll bite.

    Here is one way.

    Cheers

    Terry

      P
      ppal_25568718-Opal
      18-Opal
      May 4, 2022

      Prime 7 attached - runs on express too.

      image

       

       

       

      Plot as done by  

        F
        Fred_Kohlhepp23-Emerald I
        23-Emerald I
        May 14, 2022

        Good solution.  But it won't run in Express (no symbolics, no polyroots)

          W
          Werner_E25-Diamond I
          25-Diamond I
          May 16, 2022
          @Fred_Kohlhepp wrote:

          Good solution.  But it won't run in Express (no symbolics, no polyroots)

          Also "Minimize" (even without a solve block) is a premium function.
          But the derivative operator and the "root" function are not and you can use them for a solution in Express. You just have to manually solve a simple equation 😉

          image

           

           

          ttokoro
          21-Topaz I
          ttokoro21-Topaz I
          21-Topaz I
          May 11, 2022

          imageimageimage

          t.t.
            ttokoro
            21-Topaz I
            ttokoro21-Topaz I
            21-Topaz I
            May 16, 2022

            Prime 8 (No Express) version 2.

            Let x shows the perimeter of the circle. If x is the answer to minimize the toral area,

            imageimage

            image

             

            t.t.
            F
            Fred_Kohlhepp23-Emerald I
            23-Emerald I
            May 14, 2022

            With a node to ppal for showing the way, solving using Express (Prime 4.0)

              B
              Bodine6-Contributor
              6-Contributor
              May 16, 2022

              I contribute with an analytical approach.

               

              //cheers,

                bengt

                M
                MoeSzyslak12-Amethyst
                12-Amethyst
                May 16, 2022

                image

                 

                  P
                  ppal_25568718-Opal
                  18-Opal
                  May 16, 2022

                  Bit of labelling would be helpful. This is like a flaming Homer.

                  But Short and simple.

                   

                  Attach file please.

                  W
                  Werner_E25-Diamond I
                  25-Diamond I
                  May 16, 2022
                  @ppal_255687 wrote:

                  Bit of labelling would be helpful. This is like a flaming Homer.

                  But Short and simple.

                   

                  Attach file please.

                  Moe is using real Mathcad and this seems to be a Prime only challenge. Nonetheless I would vote for his solution being the winner.

                  BTW, because Moe's nice compact solution is using Lagrange and the Nabla operator - is the Nabla operator now finally available in Prime 8 or is it still missing?

                   

                  We could make Moe's solution even a bit more compact by using the symbolic "solve" instead of evaluating the solve block symbolically (which is something not allowed to do in Prime anyway).

                  image

                  It could even be made a one-liner (but I wouldn't suggest doing so):

                  image

                   

                  If the Nabla operator still is not available in Prime, you would have to do it the hard way

                  image

                  As usual Primes infamous auto-labeling bug required to manually re-label some variables to make it work.

                   

                  I seem to remember to have read that PTC planned to implement a partial derivative operator. While being only an optical display thing it would be appreciated. Is it already implemented in Prime 8 or was I just reading the roadmap for future versions?

                   

                   

                    L
                    LucMeekes23-Emerald IV
                    23-Emerald IV
                    May 23, 2022

                    I thought I'd add my 2 cents:

                    image

                    And since a result without an animation is not a solution....

                    image

                    Success!
                    Luc

                      P
                      ppal_25568718-Opal
                      18-Opal
                      May 23, 2022

                      I opened in mathcad 15 

                      Get errors:

                      image

                      image

                       

                      V
                      24-Ruby III
                      VladimirN24-Ruby III
                      24-Ruby III
                      May 24, 2022

                      This worksheet from 11th version of regular Mathcad.

                      D
                      DJNewman18-Opal
                      18-Opal
                      June 1, 2022

                      Thanks to everyone for your contributions; Dave will be reviewing them in short order since May is now over. I'm hoping for some good discussion and learnings to come out of it!

                      (Badges will also come soon.)

                      F
                      Fred_Kohlhepp23-Emerald I
                      23-Emerald I
                      June 9, 2022

                      No June Challenge??

                      D
                      DJNewman18-Opal
                      18-Opal
                      June 9, 2022

                      It's bimonthly, so there's been a January, March, and May challenge... and next there'll be a July.

                      C
                      chapellane1-Visitor
                      1-Visitor
                      June 20, 2022

                      I didn't use MathCAD, but having seen the solution to the original problem which has the diameter of the circle equal to the side-length of the square, I used a pencil to prove that if you share any fixed length of perimeter between a regular polygon and a circle, the circle which minimises the total area is the inscribed circle of the polygon.  Curious...

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