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- Thread starter MacCormaic
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Ben Niehoff

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$$2 + \frac{6}{\sqrt{2}} \approx 6.242\ldots$$

assuming a circle of radius 1. This is kind of close to ##2 \pi \approx 6.283\ldots##, but not especially close.

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MacCormaic

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Ben Niehoff

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jedishrfu

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http://en.m.wikipedia.org/wiki/Squaring_the_circle

There was two parts to the proof. One was that transcendental numbers can't be constructed and two was tha Pi was a transcendental number.

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MacCormaic

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What this statement says is "I wasn't trying to square the circle, I was just trying to do the same thing as squaring the circle".I wasn't trying to prove that a Circle could be squared, I was merely asking if it's possible that the circumference can be derived from another geometrical shaped placed within the circle...

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MacCormaic

No, what I asking is, is it possible that there can be a measurement between two points in a geometrical shape (or number of shapes), that when added together with a number of other measurements could make up the equivalent of the circumference of a circle. For example in the attached sketch I would assume that line A from points x + y are never absolute numbers when lines B & C are absolute; so it is possible that the percentage they are off could make them a transcendental number?

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No, what I asking is, is it possible that there can be a measurement between two points in a geometrical shape (or number of shapes), that when added together with a number of other measurements could make up the equivalent of the circumference of a circle.

Exactly. You are asking if it is possible to do the equivalent of squaring the circle.

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jedishrfu

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MacCormaic

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Exactly.

Think about it this way. If you can use a compass and ruler to construct a set of straight lines which when added up equal the circumference of a circle, you can just to this:

Using the same compass/ruler, transfer the line segments all onto one straight line. Divide that line into 4 equal parts (trivial with compass/ruler). You now have the sides of a square, the perimeter of which is the same as the circumference of the original circle. This is called squaring the circle. It is not possible.

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