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12: Hyperbolic Lane

Last updated

Sep 5, 2021
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- 11.6: Curvature
- 12.1: Conformal Disc Model

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In this chapter, we use inversive geometry to construct the model of a hyperbolic plane — a neutral plane that is not Euclidean. Namely, we construct the so-called conformal disc model of the hyperbolic plane. This model was discovered by Beltrami in [4] and often called the Poincaré disk model. The figure below shows the conformal disc model of the hyperbolic plane which is cut into congruent triangles with angles $\dfrac{\pi}{3}, \dfrac{\pi}{3}$ , and $\dfrac{\pi}{4}$ .

$截屏2021-02-23 下午1.33.26.png$

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