Abstract: This is a foundational talk on hyperbolic geometry. We will define the hyperbolic plane and geodesics for the hyperbolic plane model. The fundamental difference between Hyperbolic geometry and Euclidean geometry will be established in this talk. Our main focus will be to prove the Gauss-Bonet formula. As an immediate corollary of the Gauss-Bonet formula, we will find out the area of an n-polygon in the Hyperbolic plane model. The manifold theory is a prerequisite of this talk.
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