8cbf07d8-8f0c-4771-a082-1f7790ccbf72 25 3 5 decimal

&[DATE] &[TIME] - &[FILENAME]

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

pi [π] & Fibonacci

Simon Plouffe π  'n' incremental algorithm n pi 116 k^/ 48 k * 1 + / 28 k * 4 + / - 18 k * 5 + / - 18 k * 6 + / - (* (k 0 n sum :

13 pi 3.14159265358979

π 3.14159265358979

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n Fib 15 sqrt + (n^15 sqrt - (n^- 5 sqrt 2 n^* / : on-line Fibonacci ≡

Tom G. Fibonacci incremental algorithm n Fib i 1 n range Fib i el 15 sqrt + (i^15 sqrt - (i^- 5 sqrt 2 i^* / : idx i el i : 21 line for idx Fib augment 21 line :

n 16 :

vx n Fib 1 col : vy n Fib 2 col : XY vx vy . 13 red plotG : 31 line

n Fib XY 2 1 sys

n Fib transpose 123456789101112131415161123581321345589144233377610987216 mat

1 i 2 * π * exp / 151015 -^* i * -

1 i 2 * π * exp / abs 1

Simon Plouffe π  'n' incremental algorithm n pi 116 k^/ 48 k * 1 + / 28 k * 4 + / - 18 k * 5 + / - 18 k * 6 + / - (* (k 0 n sum :

17 pi 1086235609600600345759533260747 /

π 17 pi - 21025 -^* ≡

π 12 pi - 3.1 1019 -^* ≡

π 12 pi - 6.08 1015 -^*

13 pi float 21 convert maple 1570796327500000000 /

π 12 pi - π 13 pi - π 17 pi - 31 mat 6.081709 1015 -^* 4.103943 1015 -^* 6.205763 1015 -^* - 31 mat

1 i 2 * 12 pi * exp / 1

1 i 2 * 13 pi * exp / 121015 -^* i * -

float expansion 40 decimals 29 pi 219696086460706993143627633 /