# Largest Square Inside a Circle?



## Kevin

What's the formula for that? I assume I have to use pi or two pi somewhere but what is the formula? Seems like I should know this. I don't want a math lesson just now, only a formula for dummies. 

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Reactions: Useful 1


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## NYWoodturner

The maximum square that fits into a circle is the square whose diagonal is also the circle's diameter. The length of a square's diagonal, thanks to Pythagoras, is the side's length multiplied by the square root of two. Set this equal to the circle's diameter and you have the mathematical relationship you need. 

Thats from Google - not me. My brain hurts...:wacko1:


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## Kevin

Thanks an awful lot Scott.

Soooooo as I was saying. Anyone have a formula that I can plug numbers into?


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## Kevin

Okay I sort of found the answer and I feel stooooopid. 

_"The diagonal of the largest square that fits into a circle is equal to the diameter 'd' of the circle, so the square has sides of length a = d/sqrt(2)."_ Tim Mooney (whoever that genius is). 

So if I have a 7" circle all I got to do is lay a straight edge across my block of wood from one corner of my block to the other, and mark just below the diameter of the circle. This works fine for taking larger squares down to smaller ones, but what about blocks of wood that aren't squares? I still need a formula that will give me the max length of any square side.


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## Kevin

Joe Rebuild said:


> Kevin said:
> 
> 
> 
> Thanks an awful lot Scott.
> 
> Soooooo as I was saying. Anyone have a formula that I can plug numbers into?
> 
> 
> 
> 
> 
> 
> Would a calc that gives the cant size you can get from a log work?
Click to expand...


I don't see why not. I'd still like to know the actual formula but a calculator would be great. I have one bookmarked somewhere . . .


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## NYWoodturner

Kevin said:


> Thanks an awful lot Scott.
> 
> Soooooo as I was saying. Anyone have a formula that I can plug numbers into?



:rotflmao3: you too huh.. OK try THIS The diagonal is the same as the diameter. Should do the trick! Change the drop down mebu at the top to calculate a given q


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## Kevin

Scott I can't even figure that calculator out!


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## Bigg081

As big as you can draw.....someone has to be a smartbutt hahahah


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## Kevin

This one dumbed it down enough for me, but still looking for a shorter formula if one exists. This one so pretty short though so probably best one for ADHD patients like me. *Check it out*.

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## NYWoodturner

Kevin said:


> Scott I can't even figure that calculator out!



What is the radius or diameter of your circle?


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## Kevin

NYWoodturner said:


> Kevin said:
> 
> 
> 
> Scott I can't even figure that calculator out!
> 
> 
> 
> 
> What is the radius or diameter of your circle?
Click to expand...


The present one is 7.125 (7 1/8") ut I need an easy way to figure different sizes. And the link I just posted will not work since i don't want to have to draw everything to scale each time to figure the line AC. Sure I can hold a square across the circle but that's not what I want either.


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## hobbit-hut

Well I'm sure there are more ways than one to do it. But it sound like you need a formula that uses proportions. And that would require a math lesson. The professor is eating an apple, now he's choking on it, looks like he's being resuscitated, no - I'm afraid he's gone.


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## NYWoodturner

Kevin said:


> NYWoodturner said:
> 
> 
> 
> 
> 
> Kevin said:
> 
> 
> 
> Scott I can't even figure that calculator out!
> 
> 
> 
> 
> What is the radius or diameter of your circle?
> 
> Click to expand...
> 
> 
> The present one is 7.125 (7 1/8") ut I need an easy way to figure different sizes. And the link I just posted will not work since i don't want to have to draw everything to scale each time to figure the line AC. Sure I can hold a square across the circle but that's not what I want either.
Click to expand...


5.038 on each side if that is the diameter and not the radius


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## Kevin

NYWoodturner said:


> Kevin said:
> 
> 
> 
> 
> 
> NYWoodturner said:
> 
> 
> 
> 
> 
> Kevin said:
> 
> 
> 
> Scott I can't even figure that calculator out!
> 
> 
> 
> 
> What is the radius or diameter of your circle?
> 
> Click to expand...
> 
> 
> The present one is 7.125 (7 1/8") ut I need an easy way to figure different sizes. And the link I just posted will not work since i don't want to have to draw everything to scale each time to figure the line AC. Sure I can hold a square across the circle but that's not what I want either.
> 
> Click to expand...
> 
> 
> 5.038 on each side if that is the diameter and not the radius
Click to expand...


I had just cut a square a scosh over 5" and it fit. So your calculator or whatever you used is accurate. i guess the easy way for me to do it is to convince you to give me my own ring on your phone so when I need some numbers I can ring you up.


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## DKMD

The length of one side if the square would be the square root of two times the radius squared...

For example, a 20 inch log would have a 10" radius(r squared is 100, so 2xr is 200 thus the length of each side of the square is the square root of 200 or 14.14")


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## hobbit-hut

Looks like the Dr. resuatated the professor after all. Or maybe he is the professor. Interesting problem solved. :hatsoff:


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## ssgmeader

Kevin you can't do it with just one formula you have to use a couple.

[attachment=22081]



BC|2 + |CA|2 = |AB|2 

2 |BC|2 = 

|BC|2 =

then take the square root and 

|BC| =


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## Kevin

ssgmeader said:


> Kevin you can't do it with just one formula you have to use a couple.
> 
> 
> 
> 
> 
> BC|2 + |CA|2 = |AB|2
> 
> 2 |BC|2 =
> 
> |BC|2 =
> 
> then take the square root and
> 
> |BC| =



Adrian I had that one, it's the one where you have to draw it to scale and I don't want to do that. Thanks though. 





DKMD said:


> The length of one side if the square would be the square root of two times the radius squared...
> 
> For example, a 20 inch log would have a 10" radius(r squared is 100, so 2xr is 200 thus the length of each side of the square is the square root of 200 or 14.14")




Eureka!!!

Thanks Doc that's exactly what I was looking for. I think I can even commit that to memory.


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## BarbS

This is all much too complicated. I'd just cut out a bunch of different sized squares on cardboard and slap 'em up on the end of each log and chalk around the perimeter. if I could cut a 'little' bigger, I'd mark X's outside the line and have at it! Or use a washer to outline the perimeter beyond the square border. Does it Really have to be so accurate?


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## Kevin

It's not for logs Barb it's for more precise work otherwise that's a great idea.


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## ssgmeader

Kevin said:


> ssgmeader said:
> 
> 
> 
> Kevin you can't do it with just one formula you have to use a couple.
> 
> 
> 
> 
> 
> BC|2 + |CA|2 = |AB|2
> 
> 2 |BC|2 =
> 
> |BC|2 =
> 
> then take the square root and
> 
> |BC| =
> 
> 
> 
> 
> Adrian I had that one, it's the one where you have to draw it to scale and I don't want to do that. Thanks though.
> 
> 
> 
> 
> 
> DKMD said:
> 
> 
> 
> The length of one side if the square would be the square root of two times the radius squared...
> 
> For example, a 20 inch log would have a 10" radius(r squared is 100, so 2xr is 200 thus the length of each side of the square is the square root of 200 or 14.14")
> 
> Click to expand...
> 
> 
> 
> Eureka!!!
> 
> Thanks Doc that's exactly what I was looking for. I think I can even commit that to memory.
Click to expand...


You shouldn't have to draw it to scale you just need the diameter #as a starting point to do the math.


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