Falling off the edge of a flat world? - Not likely!

Novelists and several historians who should know better, have made a play out of the supposition that the common belief in the middle ages in Europe - pushed by the church -  was that the world was flat, and even sometimes that the trial of Galileo was about whether the earth was flat (rather than about whether the earth revolved around the sun).

The explorers of the 1400s had plenty of things to be seriously worried about (like most of them never came back), but falling off the edge of the world in the middle of the night was not one of them.  Pythagoras had shown in around 500 BC that the earth was spherical, a notion picked up later by Aristotle.  The early fathers of the church did not dispute this by then pervasive belief, despite some ambiguous statements in the bible (what's new?!).  The Northumbrian Venerable Bede went much further in terms of positive written affirmation in  the early 700s AD and was widely quoted on the subject.  On the other (flat earth) side was no authoritative voice - in fact hardly any voices at all.

Columbus' challenge was that no one knew the diameter of the earth, and thus how far he had to sail to reach China (his objective).  The diameter estimates he worked on (for example by the Florentine astronomer and mathematician  Toscanelli) were seriously less than the real figure (24,900 miles if you are interested).  Luckily for him the continents later to be known as the Americas were in the way, otherwise he pretty certainly would have disappeared from history without trace.

Then much later, in  1896, an obscure writer called Andrew Dickson White wrote a weighty tome called "The Warfare of Science with Theology" in which amongst other things he claimed that the church of the middle ages worked assiduously and successfully to propagate the flat earth theory.  Problem was that he had next to no evidence to support this.  No matter, it was a catchy "conspiracy theory" with the church as the bad boy (shades of the da Vinci Code) and achieved much more currency than it deserved, being as how it was wrong.

And as a quirky postscript a much earlier measurer, Eratosthenes, Librarian of Alexandria, wrote a treatise "On the Measurement of the Earth" (now lost) in which he gave a figure for the Earth's circumference of the equivalent of about 23,000 miles.  His method involved pacing out the distance between two points 500 miles apart, and was obviously subject to significant error limits.  Although it turned out to be 2,000 miles short of the truth, most people at the time thought that his figure was a significant overestimate.