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

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

space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces...

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

In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from...

called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line,...

four points in three-dimensional Euclidean space determine a solid figure called tetrahedron. In non-Euclidean geometries, three "straight" segments (having...

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

Polar coordinate system In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces...

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

unprovable properties on which the rest of geometry was established. Euclidean line and Euclidean geometry are terms introduced to avoid confusion with...

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...

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

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

of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space....

Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional...

Elliptic geometry Enumerative geometry Epipolar geometry Euclidean geometry Finite geometry Fractal geometry Geometry of numbers Hyperbolic geometry Incidence...

two-dimensional surfaces, and higher-dimensional objects consist. In classical Euclidean geometry, a point is a primitive notion, defined as "that which has no part"...

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

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

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

space. Several notions of a plane may be defined. The Euclidean plane follows Euclidean geometry, and in particular the parallel postulate. A projective...

topics include circles, the complex plane, inversive geometry, and non-Euclidean geometry. It was written by Hans Schwerdtfeger, and originally published in...

In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric...

ancient Greek mathematician. Euclidean space, the two-dimensional plane and three-dimensional space of Euclidean geometry as well as their higher dimensional...

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

field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories...

telegraph in 1833. Gauss was the first to discover and study non-Euclidean geometry, which he also named. He developed a fast Fourier transform some 160...

first, though a very important, step. The close axiomatic study of Euclidean geometry led to the construction of the Lambert quadrilateral and the Saccheri...

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