non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies...

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements...

century stimulated the development of non-Euclidean geometry generally, including hyperbolic geometry. Elliptic geometry has a variety of properties that differ...

hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry...

The geometry that underlies general relativity is a famous application of non-Euclidean geometry. Since the late 19th century, the scope of geometry has...

19th-century formulation of non-Euclidean geometry. The definition of the Euclidean norm and Euclidean distance for geometries of more than three dimensions...

Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally...

non-Euclidean geometries, the old postulates were re-formalized to define Euclidean spaces through axiomatic theory. Another definition of Euclidean spaces...

affine geometries and Euclidean geometry is a special instance of this type of geometry. In some other geometries, such as hyperbolic geometry, lines...

higher dimensional generalizations Euclidean geometry, the study of the properties of Euclidean spaces Non-Euclidean geometry, systems of points, lines, and...

geodesy, spherical geometry and the metrical tools of spherical trigonometry are in many respects analogous to Euclidean plane geometry and trigonometry...

Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined...

geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries...

three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and...

In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...

transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective...

the end of the 19th century, such as non-Euclidean, projective, and affine geometry. In the Greek deductive geometry of Euclid's Elements, a general line...

800 BC) – Euclidean geometry Manava (c. 750 BC–690 BC) – Euclidean geometry Thales of Miletus (c. 624 BC – c. 546 BC) – Euclidean geometry Pythagoras...

Information geometry Integral geometry Inversive geometry Inversive ring geometry Klein geometry Lie sphere geometry Non-Euclidean geometry Noncommutative...

dimensions Timeline of geometry – Notable events in the history of geometry History of Euclidean geometry History of non-Euclidean geometry History of mathematics...

mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather than flat, as in the Euclidean space. According to...

albeit different geometries. A geometry where the parallel postulate does not hold is known as a non-Euclidean geometry. Geometry that is independent...

differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry...

(ISBN 0-486-63830-8), including the subtitle Circle Geometry, Moebius Transformation, Non-Euclidean Geometry. The Basic Library List Committee of the Mathematical...

properties vary from point to point, including the standard types of non-Euclidean geometry. Every smooth manifold admits a Riemannian metric, which often helps...

two thousand years, until the simultaneous discoveries of the non-Euclidean geometries by Gauss, Bolyai, Lobachevsky and Riemann in the 19th century led...

reflections. A convex polytope is the intersection of half-spaces. In non-Euclidean geometry, the ambient space might be the n-dimensional sphere or hyperbolic...

generally, four points in three-dimensional Euclidean space determine a tetrahedron. In non-Euclidean geometries, three "straight" segments (having zero curvature)...

In Euclidean geometry, a square is a regular quadrilateral, which means that it has four sides of equal length and four equal angles (90-degree angles...

philosopher, and mathematician. He is considered the forerunner of non-Euclidean geometry. The son of a lawyer, Saccheri was born in Sanremo, Genoa (now Italy)...