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Re: ellipse, mean distance from point on perimeter to a focus ?
Posted:
Feb 11, 2010 12:22 PM
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In article <20100211111323.200$wv@newsreader.com>,
David W. Cantrell <DWCantrell@sigmaxi.net> wrote:
>Well, as Achava correctly pointed out, it depends on the variable with
>respect to which the mean is calculated.
>> Recall the "string and pins" method of drawing an ellipse, which
>> depends on the fact that the sum of the distances from a point on the
>> ellipse to the two foci of that ellipse is the major axis of that
>> ellipse. Since the sum of those two distances is always the major
>> axis, the sum of their means is the major axis.
This is true regardless of the variable.
>> By symmetry, the
>> means of these distances are the same.
So the mean will be the semi-major axis provided the variable
varies symmetrically wrt to the two foci.
(Which it doesn't for time in orbit.)
-- Richard
--
Please remember to mention me / in tapes you leave behind.
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