Rapper B.O.B. is debating your favorite astrophysicist's favorite astrophysicist Neil DeGrasse Tyson about whether the Earth is flat ...
The mistaken rapper needs to refocus his anger at Eratosthenes, because he put in work 2,000 years ago to prove that the Earth is indeed round.
How'd he do it without access to complicated machinery? He observed that a long well was completely filled with sunlight at a very specific time of year (noon on the summer solstice, when the sun is at its highest point in the sky). He correctly stated that this meant that the sun light was coming directly down onto the Earth in a straight line. Any trees, structures, etc would not cast a significant shadow since the sunlight is directly on top of them.
Since the sun is many times larger than the Earth, if the Earth is flat, sunlight would hit the Earth at a straight line across the entire "length" of the planet. However, Eratosthenes observed shadows at an angle on structures in his hometown of Alexandria, Egypt. This instantly means that sunlight hits the Earth at different angles, which means that the Earth must be curved.
So boom B.O.B., you got served.
But Eratosthenes wasn't done. He measured the angle of the shadows in Alexandria, and used it to calculate the circumference of the Earth to an astonishing precision - 25,000 miles (within 1% of the currently known value). Oh, he also invented geography.
For the nitty gritty, check out the video below from MIT via Khan Academy: