Logic doesn't say the world is flat until whatever. Until the other things happened, most people only assumed the world was flat, but logic had nothing to do with that. Accurate measurements and mathematics also were not required to logically deduce that the earth was not flat. If you see a ship sink over the horizon, you might assume it had actually sunk, but if the ship comes back to port days or weeks later, then logically you would know it hadn't sunk, and without the benefit of accurate measurements or mathematics you would know, from logic, that the earth was not flat. Finally, the idea of Columbus proving the world was round is apocraphyl; it was already common knowledge by that time.
I'd argue that it was common knowledge that the world was round by that time. It was perhaps common knowledge in the same way that evolution was common knowledge at the time of the Scopes trial, perhaps (or like it is now in my neck of the woods. 
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