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...

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

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

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...

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

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

lead to a proof of congruence. In Euclidean geometry, AAA (angle-angle-angle) (or just AA, since in Euclidean geometry the angles of a triangle add up to...

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

mathematician. It is the name of: Euclidean space, the two-dimensional plane and three-dimensional space of Euclidean geometry as well as their higher dimensional...

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...

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

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

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

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

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

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

In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely...

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

Euclidean plane, since every Euclidean plane is isomorphic to it. Books I through IV and VI of Euclid's Elements dealt with two-dimensional geometry,...

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

curves or three surfaces, called a vertex or corner. In classical Euclidean geometry, a point is a primitive notion, defined as "that which has no part"...

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

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

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...

Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area...

pseudo-Euclidean vector space (see point–vector distinction). The geometry of a pseudo-Euclidean space is consistent despite some properties of Euclidean space...

Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: If a line segment intersects two straight...

In geometry, a monogon, also known as a henagon, is a polygon with one edge and one vertex. It has Schläfli symbol {1}. In Euclidean geometry a monogon...