Beltrami-Klein model

The Beltrami-Klein model represents hyperbolic geometry within a circle, where points are inside the circle and lines are straight chords. Unlike in Euclidean geometry, parallel lines in this model can diverge or converge within the circle. Distances and angles are measured differently, reflecting the unique properties of hyperbolic space. This model visually illustrates how hyperbolic geometry deviates from flat geometry, emphasizing the idea that the parallel postulate doesn't hold in this space while maintaining straight lines as the shortest paths. It's a useful tool for understanding concepts that defy our everyday experience of space.