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Math Help - Investigate Equality

  1. #1
    Senior Member MaxJasper's Avatar
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    Question Investigate Equality

    Problem: Investigate following equality:

    \frac{2}{\pi }=\frac{\sqrt{2}}{2}   \frac{\sqrt{2+\sqrt{2}}}{2}   \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2} \text{...}

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  2. #2
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    Re: Investigate Equality

    What is there to investigate? Do you want to prove the equality? Do you want to formulate a partial product and see if it converges?
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  3. #3
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Investigate Equality

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    Re: Investigate Equality

    My thorough investigation revealed that this is Vičte's formula. Now what?
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  5. #5
    Senior Member MaxJasper's Avatar
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    Thumbs up Re: Investigate Equality

    Thanks a lot Vlasev, you are truly a good n efficient investigator...good to know the origin of the problem.
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  6. #6
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    Re: Investigate Equality

    You can define a circle to be a regular polygon with an infinite number of sides. We can define \displaystyle \begin{align*} \pi \end{align*} as the circumference of a circle of diameter equal to 1 unit. Therefore, we can get an approximation for \displaystyle \begin{align*} \pi \end{align*} by evaluating the perimeter of said regular polygon.












    Some algebraic manipulation of this will give the result you are trying to prove.
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  7. #7
    Senior Member MaxJasper's Avatar
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    Re: Investigate Equality

    This explanation is truly enlightening. Thanks a lot ProveIt.
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    Re: Investigate Equality

    That's indeed a magnificent proof!
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