Following on from what AATW has stated, surely the changing altitude of Polaris in the sky as you move south is a clue that we live on a globe. ....

Expanding upon your statement about Polaris; there are other properties of Polaris that do not work on a flat earth.  If you were to stand at the North Pole, Polaris (the North Star), would be directly overhead.  Currently Polaris is at a declination of a bit over 89 degrees.  On a flat Earth, Polaris would always be visible — no matter how far away from the North Pole you moved, it would still be above the horizon.  However, by the time you reach the equator, Polaris is on the northern horizon, and it disappears entirely once you move into the southern hemisphere. You can't see Polaris from Australia.