what does it mean when a map projection distorts the earth
Map projection However, Carl Friedrich Gauss's Theorema Egregium proved that a sphere's surface cannot be represented on a plane without distortion. The same applies to other reference surfaces used as models for the Earth. Since any map projection is a representation of one of those surfaces on a plane, all map projections distort. Every distinct map projection distorts in a distinct way. The study of map projections is the characterization of these distortions.
Early world maps Surviving texts of Ptolemy's Geography, first composed c. 150, note that he continued the use of Marinus's equirectangular projection for its regional maps while finding it inappropriate for maps of the entire known world. Instead, in Book VII of his work, he outlines three separate projections of increasing difficulty and fidelity. Ptolemy followed Marinus in underestimating the circumference of the world; combined with accurate absolute distances, this led him to also overestimate the length of the Mediterranean Sea in terms of degrees. His prime meridian at the Fortunate Isles was therefore around 10 actual degrees further west of Alexandria than intended, a mistake that was corrected by Al-Khwārizmī following the translation of Syriac editions of Ptolemy into Arabic in the 9th century. The oldest surviving manuscripts of the work date to Maximus Planudes's restoration of the text a little before 1300 at Chora Monastery in Constantinople (Istanbul); surviving manuscripts from this era seem to preserve separate recensions of the text which diverged as early as the 2nd or 4th century. A passage in some of the recensions credits an Agathodaemon with drafting a world map, but no maps seem to have survived to be used by Planude's monks. Instead, he commissioned new world maps calculated from Ptolemy's thousands of coordinates and drafted according to the text's 1st[10] and 2nd projections,[11] along with the equirectangular regional maps. A copy was translated into Latin by Jacobus Angelus at Florence around 1406 and soon supplemented with maps on the 1st projection. Maps using the 2nd projection were not made in Western Europe until Nicolaus Germanus's 1466 edition.[12] Ptolemy's 3rd (and hardest) projection does not seem to have been used at all before new discoveries expanded the known world beyond the point where it provided a useful format.[12]