topic Re: Find the area of rectangular ABCD. Green line shows half of a circle. in Mathcad

Find the area of rectangular ABCD. Green line shows half of a circle.

ttokoro — Wed, 26 Feb 2025 05:49:48 GMT

Green shows circle of half.

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

AlanStevens — Wed, 26 Feb 2025 11:20:15 GMT

My solution attached; though, as I only have Prime Express which doesn't have symbolics, I did it "by hand".

Be nice to see a solution in which Prime does the solving!

Alan

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

LucMeekes — Wed, 26 Feb 2025 13:42:37 GMT

Another handwork result.

Luc

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

Werner_E — Wed, 26 Feb 2025 15:50:17 GMT

My approach is similar to Luc's

There is no use for Mathcad's solve capabilities...

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

Cornel — Wed, 26 Feb 2025 15:26:45 GMT

@Werner_E wrote:
There is no use for Mathcad's solve capabilities...

I am wondering if there is a such a math software tool that can handle this with a solve capabilities or an automated routine (I think no). I think the only way is as solutions posted already (more with pen and paper)...

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

Werner_E — Wed, 26 Feb 2025 16:10:23 GMT

@Cornel wrote:

@Werner_E wrote:
There is no use for Mathcad's solve capabilities...

I am wondering if there is a such a math software tool that can handle this with a solve capabilities or an automated routine (I think no). I think the only way is as solutions posted already (more with pen and paper)...

Well, I think you would need an AI interface that can read and correctly interpret specification texts and can also extract the relevant information from the attached drawings and then sets up the math accordingly. Challenging ...

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

SPaulis — Wed, 26 Feb 2025 17:07:18 GMT

Here is mine. I also included a plot where the user can vary the angle with a slider. The proof comes later in the sheet.

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

SPaulis — Wed, 26 Feb 2025 18:21:22 GMT

I like the animation. What app did you use?

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

Werner_E — Wed, 26 Feb 2025 18:48:09 GMT

@SPaulis wrote:

I like the animation. What app did you use?

Mathcad, of course 😉

But 'real' Mathcad (version 15), not Prime. The sheet is attached anyway and could be converted to Prime format (but animations are not yet supported in Prime).

The AVI file created by Mathcad was converted to an animated GIF by one of the many available online converters.

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

SPaulis — Wed, 26 Feb 2025 19:13:41 GMT

Well that stinks for me!!! I guess I can use my MC15 license and set that up, but I've been concentrating on using only Prime for my engineering work. I suppose that I can always find an external web app that can do it. Our Prime wish list mist still vey heavy

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

Werner_E — Wed, 26 Feb 2025 21:34:00 GMT

@AlanStevens wrote:

My solution attached; though, as I only have Prime Express which doesn't have symbolics, I did it "by hand".

Be nice to see a solution in which Prime does the solving!

Alan

Here you are:

Unfortunately Primes symbolics does not know that the cosine of an angle from 0 to 90° is always positive.

We have explicitly tell the program that cos(theta)>0 to get the desired solution.

A strange effect occurs when we add AB>0 to the assume modifier.

The result now is a nested(!) matrix. I consider this being a bug in two respects.

Firstly, the second solution does not take into account the constraint r>0 and secondly, if there were two pairs of solutions, these would have to be output in the form of a 2x2 matrix and not in this nested form.

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

ttokoro — Wed, 26 Feb 2025 23:41:23 GMT

Thanks all. This is also 12 year's kids puzzle. So without using cos(θ) it is also solved as below.

Re: Find the area of rectangular ABCD. Green line shows half of a circle.

Fred_Kohlhepp — Fri, 28 Feb 2025 19:05:23 GMT

It's possible to do it in Prime Express, using the root function to find the angle for the radius.