function [ n_data, n, area ] = sphere_unit_area_values ( n_data )

%*****************************************************************************80
%
%% SPHERE_UNIT_AREA_VALUES returns some areas of the unit sphere in ND.
%
%  Discussion:
%
%    The formula for the surface area of the unit sphere in N dimensions is:
%
%      Sphere_Unit_Area ( N ) = 2 * PI^(N/2) / Gamma ( N / 2 )
%
%    Some values of the function include:
%
%       N   Area
%
%       2    2        * PI
%       3  ( 4 /    ) * PI
%       4  ( 2 /   1) * PI^2
%       5  ( 8 /   3) * PI^2
%       6  ( 1 /   1) * PI^3
%       7  (16 /  15) * PI^3
%       8  ( 1 /   3) * PI^4
%       9  (32 / 105) * PI^4
%      10  ( 1 /  12) * PI^5
%
%    For the unit sphere, Area(N) = N * Volume(N)
%
%    In Mathematica, the function can be evaluated by:
%
%      2 * Pi^(n/2) / Gamma[n/2]
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    19 September 2004
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Stephen Wolfram,
%    The Mathematica Book,
%    Fourth Edition,
%    Wolfram Media / Cambridge University Press, 1999.
%
%  Parameters:
%
%    Input/output, integer N_DATA.
%    On input, if N_DATA is 0, the first test data is returned, and
%    N_DATA is set to the index of the test data.  On each subsequent
%    call, N_DATA is incremented and that test data is returned.  When
%    there is no more test data, N_DATA is set to 0.
%
%    Output, integer N, the spatial dimension.
%
%    Output, real AREA, the area of the unit sphere 
%    in that dimension.
%
  n_max = 20;

  area_vec = [ ...
     0.2000000000000000E+01, ...
     0.6283185307179586E+01, ...
     0.1256637061435917E+02, ...
     0.1973920880217872E+02, ...
     0.2631894506957162E+02, ...
     0.3100627668029982E+02, ...
     0.3307336179231981E+02, ...
     0.3246969701133415E+02, ...
     0.2968658012464836E+02, ...
     0.2550164039877345E+02, ...
     0.2072514267328890E+02, ...
     0.1602315322625507E+02, ...
     0.1183817381218268E+02, ...
     0.8389703410491089E+01, ...
     0.5721649212349567E+01, ...
     0.3765290085742291E+01, ...
     0.2396678817591364E+01, ...
     0.1478625959000308E+01, ...
     0.8858104195716824E+00, ...
     0.5161378278002812E+00 ];

  n_vec = [ ...
     1, ...
     2, ...
     3, ...
     4, ...
     5, ...
     6, ...
     7, ...
     8, ...
     9, ...
    10, ...
    11, ...
    12, ...
    13, ...
    14, ...
    15, ...
    16, ...
    17, ...
    18, ...
    19, ...
    20 ];

  if ( n_data < 0 )
    n_data = 0;
  end

  n_data = n_data + 1;

  if ( n_max < n_data )
    n_data = 0;
    n = 0;
    area = 0.0;
  else
    n = n_vec(n_data);
    area = area_vec(n_data);
  end

  return
end
