Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: ellipse, mean distance from point on perimeter to a focus ?
Replies: 8   Last Post: Feb 12, 2010 5:56 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Richard Tobin

Posts: 1,267
Registered: 12/6/04
Re: ellipse, mean distance from point on perimeter to a focus ?
Posted: Feb 11, 2010 12:22 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.