Perimeter of the Ellipse (HP-15C)

[PedroLeiva]

(05-27-2021 09:59 PM)Gerson W. Barbosa Wrote:  

(05-27-2021 06:02 PM)PedroLeiva Wrote:  (differences in the 8th. decimal only, dif.=+-1)

Have you tested it for ellipses with h greater than 0.6? Although that statement should be valid for the extreme case in my examples (a = 20 and b = 0), the errors would show up starting from the fifth and sixth decimals (a =20; b = 19 and b = 18, respectively - anyway, that’s one more exact digit when compared to the approximation I have used, for these two examples).
You are using Cantrell-Ramanujan approximation, described at the end of this article.

Regards,

Gerson.

I am using Ramanujan II-Cantrell: here a & b are radius (in my PDF the input is diameter)
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