cancel
Showing results for
Did you mean:
cancel
Showing results for
Did you mean:

Community Tip - Want the oppurtunity to discuss enhancements to PTC products? Join a working group! X

Mathcad Community Challenge May 2022 - An Isoperimetric Geometry Problem

No ratings

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!

Hi,

I'll bite.

Here is one way.

Cheers

Terry

Prime 7 attached - runs on express too.

Plot as done by

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

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

Prime 8 (No Express) version 2.

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

I contribute with an analytical approach.

//cheers,

bengt

@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 😉

Using a more powerful software you may even visualize by creating an animation 😉

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

But Short and simple.

@ppal wrote:

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

But Short and simple.

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).

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

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

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?

Thats disappointing! (I assume the pic is from Prime8 )

And how about the partial derivative operator?

Yes, sorry, but as Werner indicates, I am using Mathcad 15. I remain firmly in the camp of "I'll switch to Prime when it can do everything 15 can do".

Very nice Flaming Homer reference, btw.

@MoeSzyslak wrote:

"I'll switch to Prime when it can do everything 15 can do".

Never?

Hi

Converted to Prime 8

I knew that the "grad" operator was available in the original Mathcad, but I haven't seen it in Prime.  Yet you show it in the Prime solve block, with a message that it  isn't available.

So how did Prime execute the solve block?

It didn't - its lying and cheating

This is what it really does when you ask it to recalculate:

So how did Prime execute the solve block?

The converter simply inserted a picture of the Mathcad 15 region.

Prime did  not execute the solve block. As usual for Prime it stores the results of the last calculation within its file and displays them when you open a file. The file is not recalculated automatically when you open a file (as is the case in MC15 with auto-calc on). So the result you see is the result of the last calculation done in MC15 by the converter.
This is also the reason you can use Prime Express as a reader for Prime files which use premium functions. You see what the sheet looked like in full Prime but when you try to recalculate, the premium functions will fail.
So see in ppal's answer that the recalculation in Prime yields just "Find(...)". Actually its an empty solve block without any constraint and as we know Prime won't allow to evaluate a solve block symbolically.

I thought I'd add my 2 cents:

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

Success!
Luc

Get errors:

This worksheet from 11th version of regular Mathcad.

With animation!

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!

No June Challenge??

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

Badges have been distributed to valid entrants; Dave's blog on the challenge has also been published to Mathcad.com: https://www.mathcad.com/en/blogs/community-challenge-isoperimetric-problem

Great job!

So, it seems that my entry was not "valid" because it required Mathcad 15. Alas.

The last bullet point of the guidelines thread says as much that it's a Prime-based challenge.

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...

Version history
Last update:
‎May 03, 2022 03:40 PM
Updated by:
Labels (1)