This is a bit old hat now, but nonetheless amazing. An ancient "computer" built around 87bc which could accurately calculate the movements of the Earth, moon and sun. Also solar and lunar eclipses. Possibly the planets too.
https://www.youtube.com/watch?v=p5t_mdyMQiw
http://en.wikipedia.org/wiki/Antikythera_mechanism
All the more amazing, considering that in the time of Galileo (17th century) it was still believed that the sun revolved around the Earth. Galileo of course said otherwise, but was forced under threat of torture, to recant.
Quote from: catmeow on December 30, 2012, 20:49:33
....in the time of Galileo (17th century) it was still believed that the sun revolved around the Earth.....
many ancient societies knew that the Earth was not a disk, which only proves the scientific and cultural downfall of the Middle Ages