Space geometry measures distance, angles and curvature in three dimensions. It includes elements of Euclidian solid geometry, Cartesian coordinates, topology and non-Euclidian geometry, particularly when measuring two-dimensional space on a three-dimensional object, such as a sphere. When extended to the universe, space geometry can include additional dimensions, such as time.
Ancient space geometry focused on structures and solids, such as spheres, cubes or cones, and the measurement of their volume and surface area. By the early 17th century, new concepts about space emerged and, with them, new ideas about geometry and measurements on curved surfaces. Non-Euclidian geometry emerged to address several Euclidian axioms that failed when applied to the surface of a sphere. Later, mathematicians developed these geometries to address specific types of curved surfaces. Hyperbolic and elliptical geometry, in particular, address what happens to parallel lines when applied to certain spaces. Cartesian coordinates using three dimensions also produced additional methods for measuring distance and position in space. Topology, developed in the 19th century, addresses how space behaves under deformations and changes. In the 20th Century, Einstein introduced the concept of space-time, which showed that space curves around massive objects and that time is affected as a result of this curving.