History of geometry
Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, "The Elements" is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.
Culture of Greece
The period of Classical Greece (from 800BC until the rise of Macedon, a Greek state in the north) is that most often associated with Greek advances in science. Thales of Miletus is regarded by many as the father of science; he was the first of the ancient philosophers to seek to explain the physical world in terms of natural rather than supernatural causes. Pythagoras was a mathematician often described as the "father of numbers"; it is believed that he had the pioneering insight into the numerical ratios that determine the musical scale, and the Pythagorean theorem is commonly attributed to him. Diophantus of Alexandria, in turn, was the "father of algebra". Many parts of modern geometry are based on the work of Euclid, while Eratosthenes was one of the first scientific geographers, calculating the circumference of the earth and conceiving the first maps based on scientific principles.