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#1
Old 03-09-2005, 01:52 AM
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A math question: fitting a square into a circle

I swear to Cecil I have not been in school for 8 years, so this isn't a homework question, I just have a personal little project that I'm too dumb for.


How do you figure out the measurement for the side of a square if you know the measurement for the diagonal?



(The square's gotta fit inside a circle, the points at the corners of the square rest on the circle, so I figure the diagonal of the square is equal to the diameter of the circle- right?)
#2
Old 03-09-2005, 01:55 AM
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It's the square root of two times the radius of the circle.
#3
Old 03-09-2005, 01:56 AM
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When you have a square divided by a diagonal, you have two equilateral right triangles.

Remember the Pythagorean Theorem? a2 + b2 = c2.

In this case, a=b, and you know c (the length of the diagonal). So,

2a2 = c2, where a=the length of the side, and c=the length of the diagonal.
#4
Old 03-09-2005, 01:57 AM
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Oops.
#5
Old 03-09-2005, 02:31 AM
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Quote:
Originally Posted by bienville
I swear to Cecil I have not been in school for 8 years, so this isn't a homework question, I just have a personal little project that I'm too dumb for.

How do you figure out the measurement for the side of a square if you know the measurement for the diagonal?

(The square's gotta fit inside a circle, the points at the corners of the square rest on the circle, so I figure the diagonal of the square is equal to the diameter of the circle- right?)
Don't know what a circle has to do with it. Side = diagonal/(square root of 2), in case you can't solve the equation in the prior post.
#6
Old 03-09-2005, 02:41 AM
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Quote:
Originally Posted by Smeghead
When you have a square divided by a diagonal, you have two equilateral right triangles.

Remember the Pythagorean Theorem? a2 + b2 = c2.

In this case, a=b, and you know c (the length of the diagonal). So,

2a2 = c2, where a=the length of the side, and c=the length of the diagonal.

O.K. so

the diameter of the circle / diagonal of the square is 4.75"

squared is: 22.5625"

half of which is equal to a2, right? So a2 is 11.28125"

and then a = 3.358757yadda yadda yadda (for my purposes 3 1/3 is o.k.)



Am I correct?
#7
Old 03-09-2005, 03:12 AM
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Quote:
Originally Posted by Triskadecamus
Oops.
Actually, you're correct (as are the others). According to Smeghead (correctly), 2a2=c2 (a=side of square, c=diameter of circle). So a=c / sqrt(2). Since c=2r (r=radius), a=2r / sqrt(2) = sqrt(2)r, which was your answer.
Quote:
Originally Posted by bienville
O.K. so

the diameter of the circle / diagonal of the square is 4.75"

squared is: 22.5625"

half of which is equal to a2, right? So a2 is 11.28125"

and then a = 3.358757yadda yadda yadda (for my purposes 3 1/3 is o.k.)



Am I correct?
Yep.
#8
Old 03-09-2005, 03:23 AM
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Thanks, all!
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