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...

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...

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

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...

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

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...

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

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

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...

only over short distances (relative to the strength of the gravitational field). Euclidean geometry is an example of synthetic geometry, in that it proceeds...

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...

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...

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

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...

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

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

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

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

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

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...

distance appearing in Gallai's and Kelly's proofs are unnecessarily powerful, instead proving the theorem using only the axioms of ordered geometry....

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...

Manhattan distance. Common metrics are: Euclidean distance Taxicab geometry, also known as City block distance or Manhattan distance. Chebyshev distance There...

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...