Advanced Hyperbolic Geometry 🌀
Welcome to the intriguing world of hyperbolic geometry! This branch of mathematics offers a glimpse into non-Euclidean space where the usual rules don't always apply.
The Poincaré Disk Model
The hyperbolic plane can be represented by the Poincaré disk model, where geodesics are arcs of circles orthogonal to the disk's boundary.
Unique Characteristics
- Parallel lines can diverge or converge.
- The angles of a triangle sum to less than 180°.
- Area increases exponentially with the radius.