The Museum of HP Calculators

Hyperspheres for the HP-41

This program is Copyright © 2004 by Jean-Marc Baillard and is used here by permission.

This program is supplied without representation or warranty of any kind. Jean-Marc Baillard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Overview

-"HS" calculates the hypervolume ( V_n ) and the hypersurface area ( S_n ) of an n-dimensional unit hypersphere  ( 1 < n < 188 )
-If the radius of the hypersphere equals R, multiply V_n by Rⁿ  and S_n by R^n-1

Formula:    V_n = pi^n/2/(n/2)!   ;   S_n = n.V_n
 

Program listing
 

Data Registers: /
Flags: /
Subroutines: /
 

01  LBL "HS"
02  ENTER^
03  STO Z
04  2
05  ST/ Z
06  MOD
07  1
08  +
09  X<>Y
10  INT
11  STO Z
12  LBL 01
13  CLX
14  PI
15  ST* Y
16  X<> L
17  ST/ Y
18  SIGN
19  ST- L
20  DSE Z
21  GTO 01
22  R^
23  *
24  X<>Y
25  ST* Y
26  END

( 43 bytes / SIZE 000 )
 
 

STACK	INPUTS	OUTPUTS
Y	/	Sn
X	n	Vn
L	/	n

Examples:     3  XEQ "HS"  >>>>      V₃ =  4.1888    X<>Y      S₃ =  12.5664
                   4      R/S        >>>>      V₄ =  4.9348        X<>Y      S₄ =  19.7392
            187    R/S        >>>>   V₁₈₇ =  2.7182 10^-99    X<>Y   S₁₈₇ =  5.0830 10^-97   ( in 31seconds )

-V_n is maximum for n = 5 and  S_n is maximum for n = 7.
-For n > 187 this program gives zero.
 
 
 

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