Geometry existed in Egypt and Mesopotamia, but the Greeks transformed it into a logical discipline requiring proof. The first known proof by Thales of Miletus marked a pivotal moment in the history of ideas. From then on, brilliant mathematicians like Euclid, Archimedes, Apollonius, and Pappus contributed to logic and geometry, advancing sciences such as astronomy. Greek geometry laid the foundation for scientific thought, flourishing in Alexandria until the 6th century. In the following centuries, Arab scholars translated and expanded upon Greek works, preserving and enhancing geometric...