We have seen that geometry provides a means for focusing co-axial electromagnetic radiation of all frequencies, in phase, to a point. The paraboloid, which is defined as the set of points equidistant from a fixed point (the focus) and a plane, (the directrix) is the model for a passive (therefore cheap) solution to the problems associated with communicating over great distances with micro-waves.

We have seen that the problem of placing the feed head in the path of the signal can be avoided by selecting, for the model, an off-center section of the paraboloid. This geometric solution has additional benefits, as we have noted. We have also shown the effects of using a shallow or deep dish, and that antenna gain is not dependent on the position of the focal point but only on dish diameter (aperture) and wavelength of the radiation.

The backfire design was discussed and we saw that secondary reflectors are typically either hyperbolic or elliptical in shape.

These geometric design solutions to electromagnetic wave problems are satisfying for a number of reasons. The simple forms are pleasing to the eye. The parabola has been defined and described in mathematics texts for centuries. It has had applications in classical mechanics. Electromagnetic wave theory is something quite new, yet parabolic geometry is able to resolve difficulties here too.