Inventing the Flat Earth: Columbus and Modern Historians, by Jeffrey Burton Russell, is the book for the day. Columbus did not show the world that the Earth was round. No educated European in 1492 believed that the Earth was flat. They all knew it was round. As all math geeks know, Eratosthenes of Cyrene had made a good calculation of the circumference of the Earth about 200 BCE.
Catholic church authorities did not say that the plan of Columbus to reach the orient by sailing westward was impossible because the Earth was flat. Their scholastic theology was based on the philosophy of Aristotle, who understood perfectly well that the Earth was round.
There are passages in the Bible that suggest a flat Earth, but almost all theologians of ancient and medieval times knew the evidence for a round Earth was overwhelming, and understood the Bible was not to be taken literally in this and similar cases.
The objection to the plans of Columbus was that, thanks to Eratosthenes, people had a good idea of the distance from the west coast of Europe to the east coast of China, and could easily calculate that no ship of the day could possibly carry enough supplies for the voyage.
Columbus, acting like a 21st century Republican, rejected the best science of the day and chose a smaller alternative value for the circumference that suited his purposes. He was just lucky that the Americas happened to be there. As a result their inhabitants were then horribly unlucky.
The story about Columbus and the flat Earth is a 19th century invention, not history.
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Yes, of course.
On the other hand, sometimes there is some confusion because at one time some people believed that the planet Earth is round and covered with water but that land masses are more or less flat and float in the world ocean.