import math


def directivity(aperture_efficiency, geometrical_area, wavelength):
  """
  Forward gain of an antenna over an isotropic antenna as a factor

  Given the aperture efficiency (dimensionless) and the geometrical
  area and wavelength in the same units (say, meters), this returns
  the forward or directive gain.

  @param aperture_efficiency :
  @type  aperture_efficiency : float

  @param geometrical_area : typically pi*(diam/2)^2, same units as wavelength
  @type  geometrical_area : float

  @param wavelength : same units as antenna  diameter
  @type  wavelength : float

  @return: float
  """
  return 4*math.pi * aperture_efficiency \
                   * geometrical_area \
                   / math.pow(wavelength,2)