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16-Pearl

## Mathcad Community Challenge May 2022 - An Isoperimetric Geometry Problem

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!

Dave Martin - dmartin@creowindchill.com - https://www.creowindchill.com
32 REPLIES 32
19-Tanzanite
(To:DaveMartin)

Hi,

I'll bite.

Here is one way.

Cheers

Terry

16-Pearl
(To:DaveMartin)

Prime 7 attached - runs on express too.

Plot as done by

23-Emerald I
(To:ppal)

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

24-Ruby IV
(To:Fred_Kohlhepp)

@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 😉

24-Ruby IV
(To:Werner_E)

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

18-Opal
(To:DaveMartin)

18-Opal
(To:ttokoro)

Prime 8 (No Express) version 2.

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

23-Emerald I
(To:DaveMartin)

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

5-Regular Member
(To:DaveMartin)

I contribute with an analytical approach.

//cheers,

bengt

4-Participant
(To:DaveMartin)

16-Pearl
(To:MoeSzyslak)

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

But Short and simple.

24-Ruby IV
(To:ppal)

@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?

16-Pearl
(To:Werner_E)

24-Ruby IV
(To:ppal)

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

And how about the partial derivative operator?

16-Pearl
(To:Werner_E)

Hi

Converted to Prime 8

23-Emerald I
(To:ppal)

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:

24-Ruby IV
(To:Fred_Kohlhepp)

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.

4-Participant
(To:ppal)

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.

24-Ruby IV
(To:MoeSzyslak)

@MoeSzyslak wrote:

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

Never?

18-Opal
(To:MoeSzyslak)

23-Emerald II
(To:DaveMartin)

I thought I'd add my 2 cents:

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

Success!
Luc

16-Pearl
(To:LucMeekes)

Get errors:

23-Emerald IV
(To:ppal)

This worksheet from 11th version of regular Mathcad.

23-Emerald IV
(To:LucMeekes)

With animation!

16-Pearl
(To:DaveMartin)

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!

I manage the Creo and PTC Mathcad YouTube channels for PTC, as well as all PTC Mathcad marketing in general.
23-Emerald I
(To:DJNewman)

No June Challenge??

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

I manage the Creo and PTC Mathcad YouTube channels for PTC, as well as all PTC Mathcad marketing in general.
16-Pearl
(To:DJNewman)

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!

I manage the Creo and PTC Mathcad YouTube channels for PTC, as well as all PTC Mathcad marketing in general.
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