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CTK Exchange
Max
guest
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Feb-10-06, 11:34 AM (EST) |
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"Mistake on the page (an aside, Bertrand's Paradox)"
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Dear Alexander, I found a mistake in your thoughts in the subject Bertrand's Paradox, an Aside.(https://www.cut-the-knot.org/bertrand.shtml) You wrote that the triangle divides the small circle into three EQUAL parts, but that is wrong, since the triangle divides the small cirlce in the ratio 1/5, 3/5, 1/5. (Easy prove calculating the sizes of the different areas with the formula to calculate sction areas!!) Therefore your constructions don't prove the calculated first solution!! Regards Max |
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alexb
Charter Member
2193 posts |
Feb-10-06, 11:48 AM (EST) |
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1. "RE: Mistake on the page (an aside, Bertrand's Paradox)"
In response to message #0
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I appreciate your being on alert. However, the small circle - not the disk, but the circle, the curve - is divided into 3 equal parts, exactly as the big circle is divided by the equilateral triangle. The two circles are homothetic from A.\ Also, the remark is not supposed to prove anything, but to establish the plausibility of the argument. |
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Max
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Feb-19-06, 08:39 AM (EST) |
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2. "RE: Mistake on the page (an aside, Bertrand's Paradox)"
In response to message #1
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Ok. But then it wil be easier to understand for the reader if you write that it divides the curve of the circle into three equal parts and not the cirle itself. Thank you for the prompt answer. Regards Max |
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