Perimeter of the Ellipse (HP-15C)

[Gerson W. Barbosa]

(06-04-2021 06:12 PM)Gerson W. Barbosa Wrote:  ———————

This will return exact results when y = 1:

p(a, b) ~ π(a - b)(y + 1/(4y - 1/(4y - 3/(4y - 3/(4y - 11/(12y - (4/(2y - 1) + (2592-825π)/(588-187π))))))))

Code:


…
25 C=4/(2*Y-1)+(2592-825*PI)/(588-187*PI)
…

While this forces an exact result for y = 0, it only spoils the other results.
The same happens when the 1/3 constant is used.

A better option for both 10 and 12-digit results is to discard even the 1/3 constant:

p(a, b) ~ π(a - b)(y + 1/(4y - 1/(4y - 3/(4y - 3/(4y - 11/(12y - (4/(2y - 1))))))))

Code:


…
25 C=4/(2*Y-1)
…

In C.Ret’s program just delete the steps 16 through 18 [ 3 1/x + ].