Hyperbolic Space

Hyperbolic space is a type of geometric universe where, unlike familiar flat (Euclidean) space, curves expand exponentially. Imagine drawing a triangle: in hyperbolic space, its angles add up to less than 180 degrees. Distances grow faster as you move away from a point, creating a "saddle-shaped" geometry. This space is important in areas like cosmology and advanced mathematics because it models complex structures and helps us understand spaces that are curved in ways different from our everyday experience. It offers insights into how shapes and distances behave when the usual rules of flat geometry don't apply.