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Math Help - proof of Aristarchus' Theorem geomterically

  1. #1
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    proof of Aristarchus' Theorem geomterically

    Hello,

    I have been trying to find out if 'Aristarchus' Theorem' can be solved geometrically.

    It states that if 0 < α < β < pi/2 then Sin(α)/α > Sin(β)/β

    Can you folks think of a possible way of proving this geometrically ?

    Many thanks
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  2. #2
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    Re: proof of Aristarchus' Theorem geomterically

    How about a unit circle? The length on perimeter is equals to angle theta, and the side approximating it in the right triangle will be sin(theta).

    Salahuddin
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  3. #3
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    Re: proof of Aristarchus' Theorem geomterically

    Was Aristarchus of Samos wrong because he failed to meet the burden of proof?


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