Perimeter of the Ellipse (HP-15C)
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05-27-2021, 11:28 PM
Post: #10
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RE: Perimeter of the Ellipse (HP-15C)
(05-27-2021 09:59 PM)Gerson W. Barbosa Wrote:I am using Ramanujan II-Cantrell: here a & b are radius (in my PDF the input is diameter)(05-27-2021 06:02 PM)PedroLeiva Wrote: (differences in the 8th. decimal only, dif.=+-1) H= [(a- b) / (a + b)]^2 P= π * (a+b) * [ 1 + 3H / (10+ SQRT(4-3H)) + (4/π - 14/11) * H^12] For ellipses with H>0.6, here the examples: a= 20 ----H= 0.546313800 b= 3 ----P= 82.52178335 a= 20 ---H= 0.669421488 b= 2 ---P= 81.27883093 a= 20 ---H= 0.904818560 b= 0.5 ---P= 80.11412754 For the other combinations of the radius, the results are: a= 20 ---H= 1 b= 0 ---P= 80 a= 20 ---H= 0.0006557462 b= 19 ---P= 122.5422527 a= 20 ---H= 0.00277083 b= 18 ---P= 119.4632087 Please let me know your conclusions, Pedro |
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