def METHOD_NAME():
  wavelength = 1.0 # Angstrom
  K = 1./wavelength
  print("R     K      Vsph  Vewld     D      S      V    Xroid  Vobs   o/s    S/V  Xroid/R")
  for x in range(1,21):
    radius = 0.1 * x # inverse Angstroms
    Vsph = sphere_volume(radius) # reciprocal space volume out to inverse resolution == radius
    Vewld= vol_of_Ewald_sphere_solid_of_revolution(wavelength) # reciprocal space volume
           # impacted by a complete revolution of the Ewald sphere.
    D = areaD(radius,K)
    S = areaS(radius,K)
    V = v_coordinate(radius,K)
    centroid = simplex_integration(D,S,radius,K,V).centroid
    Vobs2 = sphere_volume_minus_missing_cone(radius,wavelength)# actual reciprocal space volume
           # observed (inside Ewald sphere torus of rotation & inside resolution-limit)
    print("%5.3f %5.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f"%(
      radius,1./wavelength,Vsph,Vewld,D,S,V,centroid,Vobs2,Vobs2/Vsph,S/V,centroid/radius))
  print("At the R=2K limit, expected Vewld/Vsph ratio is [3*pi/16]=%6.3f, found %6.3f"%(
    (3.*math.pi/16.),Vewld/Vsph))
  print("At the R=2K limit, expected area D is [pi*K^2]=%6.3f, found %6.3f"%(
    (K*K*math.pi),D))
  print("At the R=0 limit, expected S/V==pi and centroid/R = 4/(3*pi) = 0.4244 [from mathworld.wolfram.com]")