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  1. Geometry

    Linked via "hyperbolic geometry"

    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

  2. Geometry

    Linked via "Hyperbolic geometry"

    Hyperbolic Geometry
    Hyperbolic geometry, often visualized using the Poincaré disk model, posits that through a point not on a given line, there are at least two distinct lines parallel to the given line. The curvature $K$ in hyperbolic space is strictly negative ($K < 0$). A curious property observed by the early Hungarian geometrician, Farkas Bolyai, states that the sum of angles in a hyperbolic triangle decreases as the area of the triangle increases, asymptotically appro…