What is "geometry"

Geometry \Ge*om"e*try\, n.; pl. Geometries[F. g['e]om['e]trie, L. geometria, fr. Gr. ?, fr. ? to measure land; ge`a, gh^, the earth + ? to measure. So called because one of its earliest and most important applications was to the measurement of the earth's surface. See Geometer.]

1. That branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines, and angles; the science which treats of the properties and relations of magnitudes; the science of the relations of space.

2. A treatise on this science.

   Analytical geometry, or Co["o]rdinate geometry, that branch of mathematical analysis which has for its object the analytical investigation of the relations and properties of geometrical magnitudes.

   Descriptive geometry, that part of geometry which treats of the graphic solution of all problems involving three dimensions.

   Elementary geometry, that part of geometry which treats of the simple properties of straight lines, circles, plane surface, solids bounded by plane surfaces, the sphere, the cylinder, and the right cone.

   Higher geometry, that pert of geometry which treats of those properties of straight lines, circles, etc., which are less simple in their relations, and of curves and surfaces of the second and higher degrees.

Mathematics \Math`e*mat"ics\, n. [F. math['e]matiques, pl., L. mathematica, sing., Gr. ? (sc. ?) science. See Mathematic, and -ics.] That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations. Note: Mathematics embraces three departments, namely:

1. Arithmetic.

2. Geometry, including Trigonometry and Conic Sections.

3. Analysis, in which letters are used, including Algebra, Analytical Geometry, and Calculus. Each of these divisions is divided into pure or abstract, which considers magnitude or quantity abstractly, without relation to matter; and mixed or applied, which treats of magnitude as subsisting in material bodies, and is consequently interwoven with physical considerations.

early 14c., from Old French géométrie (12c.), from Latin geometria, from Greek geometria "measurement of earth or land; geometry," from comb. form of ge "earth, land" (see Gaia) + -metria (see -metry). Rendered in Old English as eorðcræft.

n. 1 (context mathematics uncountable English) the branch of mathematics dealing with spatial relationships 2 (context mathematics countable English) a type of geometry with particular properties 3 (context countable English) the spatial attributes of an object, etc.

n. the pure mathematics of points and lines and curves and surfaces

Geometry is the second album by electronic musician Jega, released in 2000 on the Planet Mu label.

Geometry is an album by Brazilian jazz saxophonist Ivo Perelman featuring American pianist Borah Bergman, which was recorded in 1996 and released on the English Leo label.

Geometry (1991) is an album by the American ambient and electronic musician Robert Rich. Although completed in 1988, this album was not released until three years later.

This album is more active and structured than any of his previous works. The music was inspired in part by the complex patterns of Islamic designs like those found at the Alhambra, and features complex just intonation. The first three tracks consist of complex layered sequences of electronic notes in rich, organic-sounding chime tones. Rich revisited this style in Gaudí (1991) and Electric Ladder (2006). Tracks 4 through 7 are slow textures more common to Robert Rich’s work. The album ends with another active piece similar to the first three tracks.

Tracks 1, 2, 4 and 8 were mixed by Robert Rich and future collaborator Steve Roach at Roach’s studio in Venice, California. This album was released in a two CD set with Numena in 1997.

Geometry is a branch of mathematics dealing with spatial relationships.

Geometry or geometric may also refer to:

• Geometric distribution of probability theory and statistics
• Geometric series, a mathematical series with a constant ratio between successive terms
• Geometric (typeface classification), a class of sans-serif typeface styles

• Geometry (Robert Rich album), a 1991 album by American musician Robert Rich
• Geometry (Ivo Perelman album), a 1997 album by Brazilian saxophonist Ivo Perelman
• Geometry (Jega album), a 2000 album by English musician Jega

Geometry (from the ; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment— Euclidean geometry—set a standard for many centuries to follow. Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.

The introduction of coordinates by René Descartes and the concurrent developments of algebra marked a new stage for geometry, since geometric figures such as plane curves could now be represented analytically in the form of functions and equations. This played a key role in the emergence of infinitesimal calculus in the 17th century. Furthermore, the theory of perspective showed that there is more to geometry than just the metric properties of figures: perspective is the origin of projective geometry. The subject of geometry was further enriched by the study of the intrinsic structure of geometric objects that originated with Euler and Gauss and led to the creation of topology and differential geometry.

In Euclid's time, there was no clear distinction between physical and geometrical space. Since the 19th-century discovery of non-Euclidean geometry, the concept of space has undergone a radical transformation and raised the question of which geometrical space best fits physical space. With the rise of formal mathematics in the 20th century, 'space' (whether 'point', 'line', or 'plane') lost its intuitive contents, so today one has to distinguish between physical space, geometrical spaces (in which 'space', 'point' etc. still have their intuitive meanings) and abstract spaces. Contemporary geometry considers manifolds, spaces that are considerably more abstract than the familiar Euclidean space, which they only approximately resemble at small scales. These spaces may be endowed with additional structure which allow one to speak about length. Modern geometry has many ties to physics as is exemplified by the links between pseudo-Riemannian geometry and general relativity. One of the youngest physical theories, string theory, is also very geometric in flavour.

While the visual nature of geometry makes it initially more accessible than other mathematical areas such as algebra or number theory, geometric language is also used in contexts far removed from its traditional, Euclidean provenance (for example, in fractal geometry and algebraic geometry).