How we know the Earth is curved
It is a long-standing conspiracy theory that the Earth is not spherical but is indeed flat, and it's not hard to see why.
When you look around everything appears to lie on a flat plane. However, a preliminary consequence of my research is that the Earth has positive curvature and, moreover, we can see this using local measurements.
The tools at work behind this result eventuate in the famous Gauss-Bonnet theorem - which ultimately combines local and global results in geometry and, as a consequence, leads us to conclude that the Earth is spherical. Another interesting result is one about the right way to eat a slice of pizza, which utilises similar techniques.
Nicholas Lawson McLean