Hyperbolic geometry is geometry that plays by a different set of rules. Lines curve, triangles have less than 180 degrees, and the parallel postulate doesn't apply.

Hyperbolic plane crochet pattern: https://static1.squarespace.com/stati...
Explanation of Mobius transformations:    • Moebius Transformations Revealed  

Sections:
0:00 Intro
0:36 Gameplay
0:54 Tiling and curvature
3:14 Euclid
5:01 Poincare disc
6:36 Parallel lines
7:39 Mobius transformations
9:18 Conclusion