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Math Help - Circle

  1. #1
    MHF Contributor Mathstud28's Avatar
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    Circle

    Here is somethign I am wrestling with conceptually because it should work theoretically I think but it does not

    since A_{\text{regular polygon}}=\frac{1}{4}n\cdot{b^2}\cdot\cot\bigg(\fr  ac{\pi}{n}\bigg)

    Where n is number of sides and b is sidelength

    Shouldnt \lim_{n\to\infty}\lim_{b\to{0}}\frac{1}{4}n\cdot{b  ^2}\cdot\cot\bigg(\frac{\pi}{n}\bigg)
    Describe a circle?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Mathstud28 View Post
    Here is somethign I am wrestling with conceptually because it should work theoretically I think but it does not

    since A_{\text{regular polygon}}=\frac{1}{4}n\cdot{b^2}\cdot\cot\bigg(\fr  ac{\pi}{n}\bigg)

    Where n is number of sides and b is sidelength

    Shouldnt \lim_{n\to\infty}\lim_{b\to{0}}\frac{1}{4}n\cdot{b  ^2}\cdot\cot\bigg(\frac{\pi}{n}\bigg)
    Describe a circle?
    You don't have two limiting processes as b is determined uniquely by n, for an n sided regular polygon inscribed in the unit circle:

    b=2 \sin(\pi/n)

    RonL
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