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Math Help - another portion of dependence area of square to area of circle based on the same diag

  1. #1
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    another portion of dependence area of square to area of circle based on the same diag

    dependence diameter of square to diameter of circle based on the same diagonal is ( 4 * d / sqrt(2) / d ) to ( pi * d / d )
    area of square to area of circle based on the same diagonal is ( ( d / sqrt(2) ) ^ 2 / d ) to (( pi * d ) ^ 2 )
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    Re: another portion of dependence area of square to area of circle based on the same

    That is so "terse" it is difficult to tell what you are saying.

    A circle with diameter "d" has radius d/2 and so area \pi r^2= \pi \frac{d^2}{4}= \frac{\pi}{4}d^2.

    A square with diagonal d (so the it is inscribed in the circle) has sides of length \frac{d}{\sqrt{2}} and so area \frac{d^2}{2}.

    The ratio of "area of circle to area of square" is \frac{\frac{\pi}{4}d^2}{\frac{d^2}{2}}= \frac{\pi}{2}.
    And the ratio of "area of square to area of circle" is \frac{\frac{d^2}{2}}{\frac{\pi}{4}d^2}= \frac{2}{\pi}, the reciprocal, of course.

    But that doesn't appear to have anything to do with what you wrote. I can't make anything out of "4*d / sqrt(2) / d". What do the two "/" mean? If that was supposed to be \frac{\frac{4d}{\sqrt{2}}}{d}, that is equal to \frac{4}{\sqrt{2}}. The "d"s cancel and that certainly is not the area of the square. And why is the \pi squared in "(pi * d)^2". That is NOT the area of a circle of diameter d.
    Last edited by HallsofIvy; July 12th 2013 at 06:28 AM.
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  3. #3
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    Re: another portion of dependence area of square to area of circle based on the same

    Hello, razera!

    Sloppy wording . . . I had to guess what you meant.

    We have this scenario:
    Code:
                  * * *
              *           *
            o - - - - - - - o
           *|             * |*
            |           *   |
          * |         *     | *
          * |       o       | *
          * |     *  d      | *
            |   *           |
           *| *             |*
            o - - - - - - - o
              *           *
                  * * *


    dependence diameter of square to diameter of circle based on the same diagonal is:
    . . . ( 4 * d / sqrt(2) / d ) to ( pi * d / d ) . Why did you divide by d?

    You want the ratio of the perimeter of the square to the circumference of the circle.

    The side of the square is: \tfrac{d}{\sqrt{2}}. .Its perimeter is: 4\left(\tfrac{d}{\sqrt{2}}\right) \,=\,2\sqrt{2}d

    The circumference of the circle is: \pi d

    The ratio is . 2\sqrt{2}d: \pi d \;=\;2\sqrt{2}:\pi




    area of square to area of circle based on the same diagonal is:
    . . . ( ( d / sqrt(2) ) ^ 2 / d ) to (( pi * d ) ^ 2 ) . no

    The side of the square is: \tfrac{d}{\sqrt{2}}. .Its area is: \left(\tfrac{d}{\sqrt{2}}\right)^2 \:=\:\tfrac{1}{2}d^2

    The radius of the circle is: \tfrac{d}{2}. .Its area is: \pi\left(\tfrac{d}{2}\right)^2 \:=\:\tfrac{\pi}{4}d^2

    The ratio is . \tfrac{1}{2}d^2 : \tfrac{\pi}{4}d^2 \:=\:2:\pi
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