Category: Non-Euclidean geometry

Non-Euclidean crystallographic group
In mathematics, a non-Euclidean crystallographic group, NEC group or N.E.C. group is a discrete group of isometries of the hyperbolic plane. These symmetry groups correspond to the wallpaper groups in
Lénárt sphere
A Lénárt sphere is a educational manipulative and writing surface for exploring spherical geometry, invented by Hungarian István Lénárt as a modern replacement for a spherical blackboard. It can be us
Parallel postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-d
Elliptic geometry
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. How
Clifford parallel
In elliptic geometry, two lines are Clifford parallel or paratactic lines if the perpendicular distance between them is constant from point to point. The concept was first studied by William Kingdon C
Dehn plane
No description available.
Geometry of Complex Numbers
Geometry of Complex Numbers: Circle Geometry, Moebius Transformation, Non-Euclidean Geometry is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geomet
Saccheri–Legendre theorem
In absolute geometry, the Saccheri–Legendre theorem states that the sum of the angles in a triangle is at most 180°. Absolute geometry is the geometry obtained from assuming all the axioms that lead t
Journey into Geometries
Journey into Geometries is a book on non-Euclidean geometry. It was written by Hungarian-Australian mathematician Márta Svéd, and published in 1991 by the Mathematical Association of America in their
Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geo
Non-Euclidean surface growth
A number of processes of surface growth in areas ranging from mechanics of growing gravitational bodies through propagating fronts of phase transitions, epitaxial growth of nanostructures and 3D print
Limiting parallel
In neutral or absolute geometry, and in hyperbolic geometry, there may be many lines parallel to a given line through a point not on line ; however, in the plane, two parallels may be closer to than a