Abstract
In this chapter, we review Euclidean geometry. We begin with an informal historical account of how criticism of Euclid’s parallel postulate led to the discovery of hyperbolic geometry. In Section 1.2, the proof of the independence of the parallel postulate by the construction of a Euclidean model of the hyperbolic plane is discussed and all four basic models of the hyperbolic plane are introduced. In Section 1.3, we begin our formal study with a review of n-dimensional Euclidean geometry. The metrical properties of curves are studied in Sections 1.4 and 1.5. In particular, the concepts of geodesic and arc length are introduced.
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