Axiom 5.1.1.
Given a line and a point not on that line there exists at least two lines through the point and parallel to the line.
Section 5.1 Hyperbolic Geometry
Hyperbolic geometry results by replacing the Euclidean parallel postulate with the following.
Checkpoint 5.1.2.
There were three major variants (wordings) of the Euclidean parallel postulate. Conjecture what these look like in hyperbolic geometry.
Solution.
For Playfair’s: it is now that two or more lines are parallel to the given line. For Equidistance: the parallel line are nowhere equidistant. For Euclid: one of the sum of the angles is greater than \(\pi\text{,}\) and the other sum of the angles is less than \(\pi\text{.}\)
