function showncidea ( )

  fprintf ( 1, '\n' );
  fprintf ( 1, 'showncidea()\n' );

  close all
  figure

  x = linspace(0,2);
  y = exp(-x).*sin(2*pi*x);
  x0 = linspace(0,2,8);
  y0 = exp(-x0).*sin(2*pi*x0);
  c = InterpN(x0,y0);
  pvals = HornerN(c,x0,x);

  subplot(2,2,1)
  plot(x,y,x,zeros(1,100),'.')
  title('f(x)');
  axis([0 2 -.5 1])

  subplot(2,2,2)
  plot(x,y,x,pvals,x0,y0,'*',x,zeros(1,100),'.')
  title('The Interpolant');
  axis([0 2 -.5 1])

  subplot(2,2,3)
  plot(x,y)
  fill(x,y,[.5 .5 .5])
  title('Integral of f(x)');
  axis([0 2 -.5 1])

  subplot(2,2,4)
  plot(x,pvals)
  fill(x,pvals,[.5 .5 .5])
  title('Integral of Interpolant');
  axis([0 2 -.5 1])

  filename = 'showncidea.png';
  print ( '-dpng', filename );
  fprintf ( 1, '  Graphics saved as "%s"\n', filename );

  return
end

