Perimeter of Ellipse

[Albert Chan]

(04-12-2023 07:22 PM)floppy Wrote:  On your calc, you just stop the AGM and MAGM routines when the delta of the iteration result is good enough for you
(I stop when it is E-8; one time I tried E-9 but it went [i]ndefinitively ...

If you compare sucessive GM's or AM's (but not AM vs GM), it will not get into infinite loop.
see https://www.hpmuseum.org/forum/thread-15...#pid134773

FNP(A,B) for perimeter of ellipse, by MAGM, until full convergence of GM's

(06-04-2021 07:14 PM)Albert Chan Wrote:  10 DEF FNP(A,B) @ S=A*A+B*B @ T=1
20 REPEAT @ G=B @ K=(A-B)/2 @ B=SQRT(A*B) @ A=A-K @ T=T+T @ S=S-T*K*K @ UNTIL G=B
30 FNP = S/B*PI @ END DEF

>fnp(10, 6)
51.0539977270

Exact ellipse perimeter, rounded to 12 digits = 51.0539977268