This paper gives a summary of the history of modern geometry, from ancient Greece to the present, including a discussion of the significance of Euclid's first five postulates, emphasizing the fifth (Parallel Postulate) and how it relates to the Hyperbolic Geometry.
From the Paper:
"Many great philosophers and mathematicians worked on the study of geometry. Euclid was perhaps the most famous of these. Almost nothing is known about his life, but his famous work ,"Elements" (ca. 300 BCE) remains one of the most widely read and copied texts to this day. He gathered all of the geometrical knowledge of his time and arranged it in a logical format. (36, Levine) What distinguishes "Elements" from other works is the use of proof throughout. As far as is known, Euclid was the first person to attempt such a task. He used the Axiomatic Method to prove the correctness of the statements put forth in "Elements""
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