Introduction to Hyperbolic Geometry
Hyperbolic Geometry is an example of a geometry that negates Euclid's fifth postulate, the parallel postulate. The parallel postulate states that: "In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point."
In hyperbolic geometry, there are infinitely many lines through a point that are parallel to a given line. In this book we will work with two models of hyperbolic geometry, both models are visualized in the interior of a unit circle. In the Kline model, lines look like Euclidean lines, but angles do not look like Euclidean angles. In the Poincaré model, angles look like Euclidean angles, but lines do not look like Euclidean lines.