Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s)

01152020, 12:59 AM
(This post was last modified: 01152020 12:59 AM by Gerson W. Barbosa.)
Post: #9




RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s)
(01142020 11:47 PM)Albert Chan Wrote:(01142020 05:23 PM)Gerson W. Barbosa Wrote: Here is still another approximation to the perimeter of the ellipse: a) I simply copied it from Wikipedia ; b) Great! Thanks for your analysis, results and experimenting with Mathematica. I’ve used a much more modest tool, the hp33s Solver: XROOT(X:(A^X+B^X)÷)=C By making, for instance, A=3, B=2, C=2.52506313496 (the equivalent radius) and solving for X, I got X = 1.50125631949. The inverse of that result after the subraction of 3/2 is 795.975887056, which divided by 25 (1/h)² gives 31.8390348302. Likewise the same procedure on a couple of other examples always would return answers close to 32. Once this constant is settled, the second constant, 4, is evident: 25×32  795.975887056 = 4.02412294. And so on... 

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