Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s)
01-21-2020, 09:01 PM
Post: #14
 Gerson W. Barbosa Senior Member Posts: 1,603 Joined: Dec 2013
RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s)
(01-18-2020 03:41 PM)Gerson W. Barbosa Wrote:  p ≈ π(a + b){h²[h²(-93h² + 224) + 2304] - 4096}/{h²[h²(7h² - 544) + 3328] - 4096}

where

h = [(a - b)/(a + b)]

...

1) The wp34s program can fit in 40 steps, including LBL and END;

Actually it does fit in 38 steps:

Code:
 001:LBL A 002:⇆ XYYY 003:STO+ Y 004:©- 005:RCL/ I 006:x² 007:x³ 008:STO J 009:x⇆ L 010:FILL 011:# 007 012:×  013:# 072 014:+  015:XEQ 00 016:# 093 017:RCL× J 018:- 019:RCL× I 020:# 104 021:# 017 022:RCL× T 023:- 024:XEQ 00 025:# 007 026:RCL× J 027:+ 028:/ 029:# π   030:×  031:RTN 032:LBL 00 033:RCL× Z 034:# 128 035:-  036:# 032 037:×  038:END

Since this is the only wp34s program which is more or less optimized, I will use it as the basis for the AGM method present by Albert Chan here:

Code:
 001:LBL A 002:RCL× Y 003:z⇆ L  004:# π 005:x⇆ Y  006:× 007:STO 01 008:x⇆ L 009:√ 010:⇆ ZYYX 011:AGM 012:STO/ 01 013:x⇆ L 014:+ 015:2 016:/ 017:⇆ XYYY 018:STO+ Y 019:©- 020:RCL/ I 021:x² 022:x³ 023:STO J 024:x⇆ L 025:FILL 026:# 007 027:×  028:# 072 029:+  030:XEQ 00 031:# 093 032:RCL× J 033:- 034:RCL× I 035:# 104 036:# 017 037:RCL× T 038:- 039:XEQ 00 040:# 007 041:RCL× J 042:+ 043:/ 044:# π   045:×  046:RCL- 01 047:STO+ X 048:RTN 049:LBL 00 050:RCL× Z 051:# 128 052:-  053:# 032 054:×  055:END

Example:

Halley’s comet orbit

a = 2667950000 km

b = 678281900 km

2667950000 ENTER 678281900 A ->

p ≈ 11464318984.10299492347510528221642 km

p = 11464318984.10299540114254189105734 km

difference: 477.667 µm
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 Messages In This Thread Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 12-10-2019, 11:50 PM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Paul Dale - 12-11-2019, 01:47 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 12-13-2019, 04:08 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Ángel Martin - 01-29-2020, 11:44 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Paul Dale - 12-13-2019, 05:04 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 12-13-2019, 05:16 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 01-11-2020, 01:20 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 01-14-2020, 05:23 PM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Albert Chan - 01-14-2020, 11:47 PM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 01-15-2020, 12:59 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 01-16-2020, 04:18 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 01-18-2020, 01:14 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - grsbanks - 01-18-2020, 10:25 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 01-18-2020, 03:41 PM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 01-21-2020 09:01 PM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 01-25-2020, 02:53 AM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Paul Dale - 01-29-2020, 12:29 PM RE: Hypergeometric function – Perimeter of an Ellipse and other applications (wp34s) - Gerson W. Barbosa - 02-08-2020, 11:17 PM

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