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13: Geometry of the h-plane

Last updated

Sep 5, 2021
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- 12.9: Hyperbolic trigonometry
- 13.1: Angle of parallelism

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In this chapter, we study the geometry of the plane described by the conformal disc model. For briefness, this plane will be called the h-plane. We can work with this model directly from inside of the Euclidean plane. We may also use the axioms of neutral geometry since they all

hold in the h-plane; the latter proved in the previous chapter.

13.1: Angle of parallelism
13.2: Inradius of h-triangle
13.3: Circles, Horocycles, and Equidistants
In this section we will describe the h-geometric meaning of the intersections of the other circles with the h-plane. You will see that all these intersections have a perfectly round shape in the h-plane.
13.4: Hyperbolic triangles
13.5: Conformal interpretation
13.6: Pythagorean theorem

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