Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s)

01182020, 01:14 AM
(This post was last modified: 01182020 01:19 AM by Gerson W. Barbosa.)
Post: #11




RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s)
Here is another approximation that relies only on basic arithmetic operations and takes up less than 40 steps on HP42S/Free42, not counting the final END:
p ≈ π(a + b){h²[h²(93h² + 224) + 2304]  4096}/{h²[h²(7h²  544) + 3328]  4096} 00 { 80Byte Prgm } 01▸LBL "EL" 02 RCL+ ST Y 03 STO 01 04 X<>Y 05 LASTX 06 RCL ST Y 07 X<>Y 08 RCL+ ST L 09 ÷ 10 X↑2 11 ENTER 12 ENTER 13 ENTER 14 93 15 × 16 224 17 + 18 × 19 2304 20 + 21 × 22 4096 23  24 STO× 01 25 R↓ 26 7 27 × 28 544 29  30 × 31 3328 32 + 33 × 34 4096 35  36 X<> 01 37 RCL÷ 01 38 PI 39 × 40 END The error in the usual example (orbit of Halley’s comet) is 477.529 km, the flight distance from Rome to Milan. Use the formula or the program to check the error in the orbit of former planet Pluto (a = 5906376272 km, b = 5720637952.8 km). 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)