Nonpositive Curvature

Nonpositive curvature describes a geometric space where, unlike a sphere, the surface doesn’t curve outward. In such spaces, triangles tend to be "thinner," meaning the shortest path between two points is less than or equal to the corresponding path in flat space. This property affects how distances and shapes behave, leading to features like unique shortest paths and predictable geometric structures. Nonpositive curvature appears in advanced mathematics and geometry, providing a foundation for understanding complex spaces such as certain types of graphs, surfaces, and abstract mathematical models where "flat" or "saddle-shaped" geometries dominate.