Lobachevsky's axiom

Lobachevsky's axiom, fundamental to hyperbolic geometry, states that through a point not on a given line, there are infinitely many lines that do not intersect the original line, unlike Euclidean geometry where only one such line exists. This means space behaves differently: parallel lines can diverge, and the angles of a triangle sum to less than 180 degrees. It challenges our everyday intuition but allows mathematicians to explore geometries that model phenomena like cosmic space and complex structures beyond traditional Euclidean concepts.