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Re: The center of mass problem



Here is a more transparent, and more primitive, approach to the problem
which was presented by Tom (see below):

1. Place your curve on a graph so that the longest "diameter" is along
the x axis and its center is at x=0.
2. Measure a and b, the largest and smallest "diameters".
3. Plot an ellipse corresponding to these a and b.

If the reall ellipse and your curve coincide then the oval is an ellipse.
Otherwise it is not. You may try other sets of a and b to allow for errors,
especially if you are looking for "the best possible fit". A visual
inspection is likely to be sufficient to select the best fit. Or you can
compare individual fits in terms of "sums of the squares of differences
in y for all x". I would write a simple True Basic program to display the
two curves and to calculate "the goodness of fit" parameter for any given
a and b.
Ludwik Kowalski
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In a message dated 98-03-25 10:33:28 EST, Tom writes:

<< I have some data that forms what looks like an oval or ellipse. I would
like to fit a best curve to the points. Does anyone know of a package or
routine or a reference I could use to get to the bottom of this problem?
Thanks a lot in advance. >>

To test for an ellipse of the form x^2/a^2 +y^2/b^2 = 1, you can try this:

1. Put your x - y data into a spreadsheet.
2. Create a third column for y^2.
3. Create a fourth column for the first derivative of y^2 with respect to x,
that is d(y^2)/dx, using finite derivatives.
4. Plot d(y^2)/dx versus x. If it is an ellipse, this plot should be a
straight line with a slope of -2b^2/a^2.

Bob Carlson
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