Some 2,200 years ago, Eratosthenes calculated the radius of the Earth.
A brief recap
Plant a stick in the ground vertically, and wait until the sun is directly above the stick, that is until there is no shadow cast (or as is said to be the case historically, stand at the bottom of a very deep well in Syene and see the sun perfectly above you).
If at the same time, a friend plants a second stick in the ground in Alexandria (which was known to be about 800km from Syene), and then measures the length of the shadow, one could calculate the circumference of the Earth.
The problem I have never been able to figure out is how did Eratosthenes and his "theoretical friend" in Seyene know they were measuring the length of the shadow at the same time?
In fact, how could Eratosthenes prove that any two measurements of the sun happened "at the same time", when the primary way time was measured at the time was based on the sun?