User:Diamond Blizzard/Books/Hyperbolic Geometry: Concepts and History

Concepts and History

 * The Geometry We Know
 * Geometry
 * Euclidean geometry
 * Parallel postulate
 * Playfair's axiom


 * Strange Possibilities
 * Non-Euclidean geometry
 * Absolute geometry
 * Hyperbolic geometry


 * Concepts Related to Hyperbolic Geometry
 * Limiting parallel
 * Ideal point
 * Ultraparallel theorem
 * Gaussian curvature
 * Angle of parallelism
 * Hypercycle (geometry)
 * Horocycle
 * Hyperbolic triangle
 * Angular defect
 * Ideal triangle
 * Apeirogon
 * Uniform tilings in hyperbolic plane
 * List of regular polytopes and compounds
 * Coordinate systems for the hyperbolic plane


 * Historically Important People and Ideas
 * Nikolai Lobachevsky
 * Carl Friedrich Gauss
 * Eugenio Beltrami
 * Henri Poincaré
 * Sphere-world
 * Proclus
 * Ibn al-Haytham
 * Giovanni Girolamo Saccheri
 * Saccheri quadrilateral
 * Omar Khayyam
 * Johann Heinrich Lambert
 * Lambert quadrilateral


 * Is This Relevant to Our World?
 * Hyperbolic space
 * Special relativity
 * Geometrization conjecture
 * Shape of the universe


 * Models of Hyperbolic Geometry and Why We Need Them
 * Hilbert's theorem (differential geometry)
 * Pseudosphere
 * Beltrami–Klein model
 * Poincaré disk model
 * Poincaré half-plane model
 * Hyperboloid model
 * Band model


 * Artistic Depictions of Hyperbolic Geometry
 * M. C. Escher
 * Circle Limit III
 * Mathematics and fiber arts
 * Truncated order-7 triangular tiling
 * HyperRogue
 * Flatterland