Distance geometry is the branch of mathematics concerned with characterizing and studying sets of points based only on given values of the distances between...

the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras. In the Greek deductive geometry exemplified by...

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

Euclidean geometry, the distance between two points A and B is often denoted | A B | {\displaystyle |AB|} . In coordinate geometry, Euclidean distance is computed...

concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest...

a given point in a plane by using a distance and an angle as its two coordinates. These are the point's distance from a reference point called the pole...

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

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

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...

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

there are other notions of distance (such as the Manhattan distance) for which this property is not true. In the geometries where the concept of a line...

solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic...

defines some notion of size, distance, shape, volume, or other rigidifying structure. For example, in Riemannian geometry distances and angles are specified...

Computational geometry is a branch of computer science devoted to the study of algorithms that can be stated in terms of geometry. Some purely geometrical...

Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of...

use of squared Euclidean distance "has often been found convenient elsewhere"; for instance it is used in distance geometry, least squares statistics...

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

In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts...

matrix is a Euclidean distance matrix for some n + 1 points in the field of distance geometry. Karl Menger was a young geometry professor at the University...

(1995), "Computing the Fréchet distance between two polygonal curves" (PDF), International Journal of Computational Geometry and Applications, 5 (1–2): 75–91...

Polar distance (geometry), more correctly called radial distance, typically denoted r, a coordinate in polar coordinate systems (r, θ) Polar distance (botany)...

Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of...

Geometry of Distance is an album by cellist Tomeka Reid, vocalist Kyoko Kitamura, cornetist and trumpeter Taylor Ho Bynum, and guitarist Joe Morris. It...

quantum gravity, quantum geometry is the set of mathematical concepts that generalize geometry to describe physical phenomena at distance scales comparable to...

complementary information including relative distances, dihedral angles, angles, and connectivity. Molecular geometries are best determined at low temperature...

Chebyshev distance is a metric induced by the supremum norm or uniform norm. It is an example of an injective metric. In two dimensions, i.e. plane geometry, if...

With Arthur Cayley, Menger is considered one of the founders of distance geometry; especially by having formalized definitions of the notions of angle...

mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known...

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an...

to express distance in terms of a projective metric, and related them to general quadrics or conics serving as the absolute of the geometry. Klein (1871...