Geometry

Geometry is a branch of mathematics 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 branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.

thumb|right|A right-handed three-dimensional Cartesian coordinate system used to indicate positions in space|class=skin-invert-image

thumb|upright=1.25|Symmetry (left) and asymmetry (right) thumb|upright=0.8|A spherical symmetry group with [[octahedral symmetry. The yellow region shows the fundamental domain.]] thumb|upright=0.8|A fractal-like shape that has [[reflectional symmetry, rotational symmetry and self-similarity, three forms of symmetry. This shape is obtained by a finite subdivision rule.]]

geometric line segment whose endpoints both lie on the curve

transformation of a body from a reference configuration to a current configuration

idea in geometry

mathematical space setting which eases explanation of special relativity

type of geometry

interference pattern

describing crystal lattice planes

function from a set having some geometric structure to itself or another such set

group of transformations under which the object is invariant

graph of space and time in special relativity

modern implementation of the method of indivisibles

history of the mathematical discipline of geometry, one of the two premodern fields of mathematics (together with arithmetic)

right|210px|thumb|Trilateration in three-dimensional geometry right|150px|thumb|Intersection point of three pseudo-ranges Trilateration is the use of distances (or "ranges") for determining the unknown position coordinates of a point of interest. When more than three distances are involved, it may also be called multilateration, for emphasis. The point of interest is often around Earth (geopositioning).

series of string figures elaborated between two or more people as a game

American award for geometry or topology research

theorem that, in Euclidean geometry, the sum of angles of a triangle is π radians

oriented planes

thumb|right|An RG-59 coaxial cable thumb|right|Coaxial "disks" around their common axis

mathematical idealization of the surface of a 3D body

the box or hyperrectangle of minimal dimensions that contains the set of interest

area of all the sides of the object, excluding the area of its base and top

rules related to the mathematical principles of origami

Domain in a Euclidean space whose boundary is sufficiently regular

thumb|Notional amplituhedron visualization In mathematics and theoretical physics (especially twistor string theory), an amplituhedron is a geometric structure introduced in 2013 by Nima Arkani-Hamed and Jaroslav Trnka. It enables simplified calculation of particle interactions in some quantum field theories. In planar N = 4 supersymmetric Yang–Mills theory, also equivalent to the perturbative topological B model string theory in twistor space, an amplituhedron is defined as a mathematical space known as the positive Grassmannian.

geometric property of a pair of sets of points in Euclidean geometry

study of geometric properties of sets through measure theory, extending differential geometry to not necessarily smooth sets

feature of reference (point, line, plane, hole, set of holes, or pair of surfaces) against which some others are calculated

thumb|right| Figure 1. Basic fractal patterns increasing in lacunarity from left to right. thumb|right| The same images as above, rotated 90°. Whereas the first two images appear essentially the same as they do above, the third looks different from its unrotated original. This feature is captured in measures of lacunarity listed across the top of the figures, as calculated using standard biological imaging box counting software .

Graphical method for the real roots of a polynomial

geometry Theorem

metric space in which every two points are connected by a unique geodesic arc

mathematical abstraction of the real-life notion of visibility

concepts from applied mathematics, computer science and engineering to design efficient algorithms for complex 3D models.

award to highlight outstanding contributions by women in the field of topology and geometry

the space surrounding an object

in GIS, a zone around a map feature measured in units of distance or time, useful for proximity analysis

an operation applied to a polyhedron

right|400px|thumb|Superellipsoid collection with exponent parameters, created using POV-Ray. Here, e = 2/r, and n = 2/t (equivalently, r = 2/e and t = 2/n).

formal generation of a geometrical figure using idealized mathematical instruments

right|300px|thumb|Some superquadrics. In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs.

Superspace is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions x, y, z, ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numbers rather than real numbers. The ordinary space dimensions correspond to bosonic degrees of freedom, the anticommuting dimensions to fermionic degrees of freedom.