Geometry

Ancient civilizations developed a numerical (emprical) mathematics to solve practical problems. When not used for simply counting herds or flocks, the Egyptians and Babylonians both invented whole numbers, fractions, arithmetic, and geometric relationships sufficient for commerce, administration, taxes, astronomy, determining of seasons,  and large engineering works. The historian Herodotus states that geometry was the gift of the Nile since it wiped out boundaries, requiring annual surveying of the land. The classical Greeks went beyond the empirical by stressing the use of reason.  In the 7th century BC Greek mathematicians, beginning with only a few basic geometric concepts, developed thousands of new mathematical relationships based solely on reason, not experience.  Here are some of them:

Thales of Miletus

Foundations of Greek Geometry
The Day the Universe Changed

Pythagoras

Generalization of the Pythagorean Theorem
Proof of Pythagorean Theorem
Grandfathers of Geometry

Euclid

The Return of Odysseus and the Elemants of Euclid
Euclid's Biography

Archimedes

Drexel University - Archimedes
Archimedes' Method of Estimating Pi
Archimedes of Syracuse

Apollonius of Perga

Apollonius of Perga
Apollonius

Eratosthenes of Cyrene

Eratosthenes
Sieve of Eratosthenes
The University of Utah-Eratosthenes

Hypatia

The Life of Hypatia
Agnes Scott College - Hypatia

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