# The Squared Circle

Discussion in 'Physics & Math' started by Motor Daddy, May 7, 2022.

1. ### Motor DaddyValued Senior Member

Messages:
5,425
Up for discussion is this beautiful pic of a squared circle, sporting 3.14159 square units of area for the circle, and 1.77... units of side length for the square. The radius of the circle is 1 unit.

I was wondering is someone here could verify the square's side length using Trig. Two decimal places should be sufficient for a "close enough" representation of a squared circle, right?

3. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

Messages:
10,000
The picture is misleading, and not representing the geometry of a squared circle. Looking at the image, basic trig would put the length of the square at ✓3, and not ✓pi. So it's a reasonable approximation, but no cigar.
It's not thought to be possible to square the circle through any such geometric means, but you can give it a try.

5. ### Motor DaddyValued Senior Member

Messages:
5,425
It is not the square root of 3.

I put this on a math forum, and someone posted it was 1.77... with a diagram showing the trig. If you think it is 1.73 show your work!

7. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

Messages:
10,000
I'm saying it is NOT 1.73... but that the diagram as drawn suggests it is. I.e. the diagram is inaccurate, and shows a way to get an approximation.

Basic trig from the diagram can show that the diagram suggests the length is ✓3 (i.e 1.732...) when it should be ✓pi (i.e. 1.77....). I can't post any pictures to show how the diagram suggests ✓3 at the moment, but if you're not capable of working it out yourself (it really is quite basic) in the meantime then I'll try and post something tomorrow when I'm at my pc.

Messages:
5,425
9. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

Messages:
10,000
Which diagram, and what about it? I'm not going to read a thread from another website and continue that discussion here. If you want to say something, say it. Please don't just point to another thread on a different website and go "look at that!".

10. ### Motor DaddyValued Senior Member

Messages:
5,425
You claimed the pic shows the side length to be the square root of 3. I am showing you a link that has the proof that it is 1.77... If you choose to ignore that, great, but do not continue your BS about it being the square root of 3, because it is NOT!

Put your blinders on if you must, but do not continue to spew BS once you close your eyes to the truth!

11. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

Messages:
10,000
If the link suggests 1.77... then it is either not the same diagram or the calculation in that other forum/website is wrong. Period. No blinkers required.
Now, as said, I'll try and post the trig tomorrow, but I'd have thought that even you can work it out from the diagram above in the OP. If you're unable then you'll just have to wait, I guess.
Goodnight.

12. ### Motor DaddyValued Senior Member

Messages:
5,425
It is the same diagram, and the poster posted a diagram of the proof, and how he calculated it. He showed his work with the diagram. If you choose to ignore that, that's your problem!

13. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

Messages:
10,000
If you have the proof that it's 1.77...., and details of how he calculated it, why ask here?

Anyhoo - now that I've seen the picture in more detail (larger and clearer screen than on my phone last night) it seems that the edge of the square lies just outside the intersection point of the two circles, so the length will be very slightly larger than root-3.
I had assumed from what I saw that the edge lay on the intersection, which basic trigonometry would then tell you means a length of root-3.

But given that you have the proof of the 1.77... in the other website, I'm sure you'll be happy going there for it rather than anyone bother to repeat it here for you.

14. ### James RJust this guy, you know?Staff Member

Messages:
38,326
Why are you asking us to repeat analysis that has already been done for you by somebody else?

15. ### James RJust this guy, you know?Staff Member

Messages:
38,326
There's no problem with producing a diagram which has a circle and a square of approximately equal area. The "squaring of the circle" problem, however, requires that you do it exactly, using only a pair of compasses and a straightedge.

So, what we need to know when somebody claimed to have "squared the circle" is the step-by-step procedure that could be used to construct the relevant square and circle, using only compass and straightedge. We are allowed to assume that lines constructed using these tools have no thickness etc. What is important is the procedure.

The conjecture is that it is impossible to square the circle using only compass and straightedge. A counterexample giving an appropriate method would disprove this conjecture.

I dimly seem to recall that there is a mathematical proof that such a construction, using only compass and straightedge must be impossible. If that proof is valid, then anybody claiming to have done it is either telling lies or has made a mistake somewhere (meaning they haven't actually achieved the result they think they achieved).

I note that the opening post of this thread does not specify how the diagram was constructed, or even whether it could be constructed using only compass and straightedge. Nor does it specify the steps in the supposed construction.

16. ### Motor DaddyValued Senior Member

Messages:
5,425
I'm trying to get a second opinion. It turns out that was a good idea, as Sarkus seems to think the side length is 1.73 when it has been analyzed and measured to be 1.77 on a math forum.

Just goes to show you that a second opinion is always a good idea.

17. ### Motor DaddyValued Senior Member

Messages:
5,425
So what is your final verdict on the side length, that it is not 1.73? If you acknowledge that it is not 1.73 then what do you measure the length to be, using Trig? Can you show your work?

How about an apology to me for making false claims about it being 1.73, and making a nasty comment like "it really is quite basic" implying I am too stupid to see how it can be 1.73, when in reality now you acknowledge that it is in fact NOT 1.73?

18. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

Messages:
10,000
There was no such implication, only that the trig to show 1.73... is basic so you shouldn't need me to tell you. If I thought you were stupid I would have spelt it out for you.

19. ### Motor DaddyValued Senior Member

Messages:
5,425

The trig does NOT show it to be 1.73, so it's YOU that needs to have that spelled out to you!

Are you refusing to apologize to me for making false claims that the side length is 1.73? You refuse to admit that you were wrong?

20. ### Motor DaddyValued Senior Member

Messages:
5,425
Warning: Sarkus is posting false information in the Physics & Math forum!

Last edited: May 8, 2022
21. ### Motor DaddyValued Senior Member

Messages:
5,425
Reported for making false statements in the Physics & Math forum.

22. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

Messages:
10,000

I have already admitted my mistake, and explained the error, if you bother to read. Instead you seem to want to make an issue out of it. I'm not playing that game with you.
So ttfn.

23. ### Motor DaddyValued Senior Member

Messages:
5,425
You gave an excuse for making a claim, but you did not apologize to me for making a false claim. You never retracted the claim that Trig claims it to be 1.73. You made a claim that it was "basic" when it fact it was not!

You owe me an apology, and you owe the readers an apology for making false claims in the Physics & Math forum! Maybe YOU should go back to school and learn the "basics."

Your post should be deleted and you should be warned for posting BS in the Physics & Math forum, just like everyone is treated on this forum that posts BS!!

Last edited: May 8, 2022