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1. Geometry

   Linked via "parallel postulate"

   Foundational Axiomatics and Historical Context
   Classical geometry is often traced to the work of Euclid of Alexandria, whose Elements codified plane geometry and solid geometry around 300 BCE. This system was fundamentally rooted in five postulates, the fifth of which—the parallel postulate—later became the source of significant mathematical upheaval.
   The axiomatic stability of Euclidean space relies on the concept …

2. Geometry

   Linked via "parallel postulate"

   Non-Euclidean Geometries
   The rejection or modification of the parallel postulate gave rise to non-Euclidean geometries in the 19th century, most notably hyperbolic geometry and elliptic geometry (also known as Riemannian geometry).
   Hyperbolic Geometry