Though it seems difficult to comprehend, there are apparently still people who, in all seriousness, believe that the world is flat, and all evidence presented to the contrary is just part of a huge conspiracy.   The recent documentary “Behind the Curve” follows the lives of a few prominent flat earthers (the Flat Earth Society of course takes issue).

On the other hand, there is a flat-earth misconception that many scientific skeptics hold:  that is that prior to Columbus, even well-educated people thought the earth was flat (and that the Roman Catholic church considered that the idea of a spherical earth was heretical.   On the contrary, as explained by science historian Thony Christie :

Back in the third century BCE the astronomer mathematician Eratosthenes from Alexandria determined the size of the sphere using the angle of the sun’s shadow and a bit of basic trigonometry. He achieved a fairly accurate result, its accuracy depends on which Stadia (an ancient measure of length) you think he used; we don’t know for certain. Other geographers and astronomers also determined the size of the earth’s sphere; all arriving at reasonable ball park figures. Ptolemaeus, in his Geōgraphikḕ (Geography) also determined that the known land area the oikoumenè, Europe, Africa and Asia, stretched over 180° of the earth’s surface from east to west.

In the High Middle Ages, Europe regained this knowledge, largely via the Islamic Empire through Spain and Sicily. The standard European university astronomy text Johannes de Sacrobosco’s De sphaera mundi, written in the twelfth century CE, contained all the standard Greek arguments for a spherical earth including the lunar eclipse shadow, ship breasting the horizon and the change in visible asterism travelling from south to north. There existed no doubt amongst the educated in the Middle Ages that the earth was a sphere.