I really like this clip from Carl Sagan's show Cosmos, about 3rd century BC ancient Egyptian scientist Eratosthenes (previously at BB).
Eratosthenes not only figured out that the Earth was round by observing the difference between the length of shadows in two different places at the same time of day, but accurately calculated the circumference of the Earth.
Sagan very clearly explains how he did it, and you can definitely understand Eratosthenes's method, and marvel at its genius, by watching this six minute video.
"Eratosthenes's only tools were sticks, eyes, feet and brains. Plus a zest for experimenting. With those tools, he correctly deduced the circumference of the Earth, to high precision. With an error of only a few percent. That's pretty good figuring for 2,200 years ago."