The Piri Reis Map of 1513 is a typical portolano in appearance. The usual portolan chart is characterized by groups of eight, sixteen, or thirty-two lines radiating from one or more centers on the chart, like the spokes of a wheel. These lines, or rhumbs, are equally spaced at angles of 45, 221/2 or 111/4 degrees apart. It has hitherto been supposed that this system of radial lines originated as actual course lines between various ports, that is, compass courses. It has not been supposed posed that any mathematical system underlay these portolan charts.
It is this assumption that has now been destroyed by the discoveries made by Professor Hapgood and his students. They have proved that, in the cases of several of these maps, the portolan design is based on geometry and may be translated by plane or spherical trigonometry into the terms of modern latitudes and longitudes.
Charles H. Hapgood. Maps of the Ancient Sea Kings: Evidence of Advanced Civilization in the Ice Age (Kindle Locations 2342-2347). Kindle Edition.