Talk:Perimeter of an ellipse
Confusing numerical solution
[edit]I've been trying to numerically integrate various astronomical examples of ellipses, using the expression given ("sum from i=1 to infinity of" blah blah) and finding that it diverges at shapes (eccentricities) greater than 0.5. Which isn't what you want for a series that going to converge to a real value.
I think I've found my error of understanding - in that section the "a" and "b" parameters are defined as major and minor diameters of the ellipse. BUT the diagram at the top of the page uses the same term for the semi-diameters (I'm not sure "radius" would be the right term).
Is my confusion appropriate, or is there some other problem that I haven't noticed?
From Wiki:ellipse, I see (as I'd thought) that "Analytically, the equation of a standard ellipse centered at the origin with width 2a and height 2b is: ... ", which again is not the terminology used in the infinite series section.
Should it matter? I'm not sure - it's probably because I'm taking my astronomical data from perihelia and aphelia to get the eccentricities. And being off by a factor of 2 somewhere would fit with the error becoming apparent at eccentricity greater than 1/2.
Ho hum, back to the grindstone. RTFreferences.
AKarley (talk) 18:02, 21 December 2024 (UTC)