3 Equations - 3 Variables

[mgodoytomazela]

Hello guys,

   I'm doing a geometrical calculation program in excel, and for that, I'm using Mathcad to define the formulas.

   For the last one, I have 3 known distances in R3, and 3 coordinates, and I want to find the last one.

   So , the formulas are:

    All the variables are input given, but (a, b, d), which are the last point coordinates (x,y,z).

    I need to get the formulas, a, b, d only in function of the given variables.  So a symbolic solution someway like that:

    a = t+ w-j +2 o.....

    b = o+ n-j +2 w.....

    c = w+ t-j +2 j.....

   I'm very unexperient with Mathcad, so I don't know any function that could do this automaticly for me.  

[LucMeekes]

Seems like a simple question. The answer is not easy. My computer is crunching at the moment.

I suspect that IF it gives an answer, you will not like to implement it in excell, as it's going to be big formulae.

Anyway. I suspect that you are looking for fully real answers ( all imaginary parts equal to zero ), am I right?

Luc

[mgodoytomazela]

You are right. As it's a geometrical problem, I'm not looking for imaginary numbers.

[LucMeekes]

Here you go:

Now we need to get the three (?) components.

[mgodoytomazela]

Hey Luc, thank you.

If the formula is huge, I can split it in various short parts to write in excel. This will be no problem.

I'm getting the same error! I really don't matter if it's 1 meter lenght, but I need the formulas.

[LucMeekes]

I'm afraid it's not symbolically solvable. Here you have part of an anaylsis:

And it goes on like:

The expression above is about 7 pages wide. Then to calculate d gives an expression that is too big to copy into this field, I cannot even find a way to count the pages, but I'm guessing it's over 50 pages wide....for two possible values of d (due to the squares)... and they aren't explicit... d still depends on b and a....

For symbolics I think you're out of luck here.

But once you fill in numbers, there's little trouble to get answers. Here's an example:

Note that there are 2 solutions each for a, b and d. The top row holds one set of them, the bottom row holds the other set.

Considering you know the numbers, I'd suggest you do the calculation in Mathcad.

Success!

Luc

[ValeryOchkov]

[mgodoytomazela]

Valery, can you please send me your file?

There are somethings that I'm not understanding.

[ValeryOchkov]

See the attach and Этюд 13. Путешествие окружности в треугольнике, а треугольника в ложбине или Сам себе компьютерный режиссер

[AlanStevens · Accepted solution]

By predefining some constants you can get a symbolic representation of the solutions for a, b and d.  See how these are developed in the attached.

Alan

[Werner_E]

Alans solution is brilliant as usual but I wonder why you would use Excel at all. Why don't you do all your calculations completely in Mathcad using a numeric solve block at the end?

If you insist on Excel you may consider using Excels Solver to do the job.

[AlanStevens]

Werner Exinger wrote:

...I wonder why you would use Excel at all. Why don't you do all your calculations completely in Mathcad using a numeric solve block at the end?

...

My view entirely!

Alan

[mgodoytomazela]

Thank you all guys for the effort. This is the first time I'm using this forum, and I very glad with what I'm seeing here. You are really awesome.

Alan, I've opened your file yesterday. It's seens brilliant indeed. I'm going to take a look today, understand and make the transportation to excel, and I come here with a feedback.

Werner, this spreadsheet is gonna be an official software tool for the enginners that will make the project of one line of our products, using the calculation. We have very limited Mathcad, and infinite Excel licenses. So, as we are going to use the software worldwide, there is unfortunately no way to do it in Mathcad.

[mgodoytomazela]

Alan,

Just a small detail on the end.

d1 = k4 * (k5 + k6) - k3

d2 = k4 * (k5 - k6) - k3

But the system worked perfectly. Thank you so much.

[AlanStevens]

Oops!  I sometimes (often!) make silly mistakes.  That's why it's essential to check for yourself.

Alan

[mgodoytomazela]

Alan,

I'm having problem to solve a similar equation with your method. It's a little bit more complicated and I'm not being able to handle it. Can you help me?

[mgodoytomazela]

A little mistake in the first formula:

Still not solving.