10 Axiomatic Geometry

While the word geometry is derived from ancient Greek words meaning to measure the Earth, the mathematical subject of geometry involves a mixture of theoretical structures and applicable ideas. Egyptian and Babylonian geometry primarily derived from observation, experimentation, and some deductive reasoning to discover relationships between the diameter and circumference of a circle, the Pythagorean theorem, and basic trigonometric relationships. However, the ancient Greeks blended this geometry of measurement centered on applications with their love for logic and reasoning to create the axiomatic system of geometry found in Euclid’s Elements. The foundational idea of the Elements involves the development of a logical system built upon basic accepted elements of definitions, common notions, and postulates.