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CTK Exchange
Lloyd Marks
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Aug-03-08, 05:58 PM (EST) |
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"concerning pi"
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I think I found an accurate method that converts the area of a circle into a square using only compass and straight edge. All I need to know is if the value 22/7 is an accurate value to use for pi. |
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Douglas Ort
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Aug-22-08, 08:21 AM (EST) |
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3. "RE: concerning pi"
In response to message #0
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Why do people try to do the impossible? If you could "square the (unit) circle", you would have a square with side length the square root of pi. It's a well known theorem that any length that can be constructed from a segment of unit length with ruler and compass is an algebraic number. Consequently, the square root of pi, hence pi itself, would be an algebraic number, contrary to the well known theorem that pi is transcendental.
As far as constructing a square which is "approximately" that of a circle, it is hardly a daunting problem. You can construct a square as close to the circle's area as you wish. Just use a binary approximation to the square root of pi to any accuracy you wish, construct a segment of that length and erect a square on it. |
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