A Physical Fraction

The Piri Reis map is a famous pre-modern world map compiled in 1513 from military intelligence by the Ottoman - Turkish admiral and cartographer Piri Reis. The half of the map which survives shows the western coasts of Europe and North Africa and the coast of Brazil with reasonable accuracy. Various Atlantic islands including the Azores and Canary Islands are depicted, as is the mythical island of Antillia and possibly Japan. The map has been used to claim an ancient knowledge of an ice-free Antarctica, transmitted either from extra-terrestrials or an Ice Age civilization. These claims are generally considered to be pseudo-scholarship, and some scholarly opinion is that the region sometimes thought to be Antarctica is more likely to be Patagonia or the Terra Australis Incognita (Unknown Southern Land) widely believed to exist before the Southern Hemisphere was fully explored.

Charles Hapgood began studying the map in the middle of the 20th century. Hapgood claims this and other maps support a theory of global exploration by a pre-classical undiscovered civilization. He supports this with an analysis of the mathematics of ancient maps and of their accuracy, which he says surpassed instrumentation available at the time of the map's drafting.
Hapgood argued that owing to the map being assembled from components, the Caribbean section was rotated nearly 90º from the top of South America. He attributed this to either copying from a polar projection, or to fit in the space available by hinging the map at that location and giving it an "alternate north" of which other examples are known in maps of the era.