tags: #publish links: [[Mathematics]], [[Meta - Why is this place called Hyperbolic Cloud]] created: 2021-07-17 Sat --- # Hyperbolic Geometry https://en.wikipedia.org/wiki/Hyperbolic_geometry A geometry that has negative curvature. This means there's a whole lot more space. It kind of gets more spacious the further you travel. Imagine a line, and a point off to the side. In "normal" (Euclidean) geometry, you'd only be able to draw one line through that point that didn't intersect the other line: the parallel line. In hyperbolic geometry, there's lots of possible lines through that point that don't intersect the other line, as they tend to kind of diverge the further away you go. Circles have a bigger circumference than you'd expect. Generally there's plenty of room out there and you might get lost long before you get to infinity...