Comparing and Contrasting Euclidean, Spherical, and Hyperbolic Geometries
The first issue that I will focus on is the definition of a straight line on all of these surfaces. For a …show more content…
The next issue that I will address for these three geometries is the definition of an angle on all three surfaces. The definition that I will give applies to all three surfaces. There are at least three different perspectives from which we can define “angle”. These include: a dynamic notion of angleangle as movement, angles as measure, and angles as a geometric shape. A dynamic notion of angle involves an action which may include a rotation, a turning point, or a change in direction between two lines. Angles as measure may be thought of as the length of a circular arc or the ratio between areas of circular sectors. When thinking of an angle as a geometric shape an angle may be seen as the delineation of space by two intersecting lines. I have provided my homework assignment on my definition of an angle so that one can see the reasoning of my definition for all three surfaces. However, my homework assignment does not ask to define an angle on a hyperbolic plane. This is because a region on a hyperbolic plane

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