Geometry: Difference between revisions
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In common parlance, '''geometry''' is a branch of mathematics that studies the relationships between figures such as [[point (geometry)|points]], [[line (geometry)|lines]], [[polygon]]s, [[solid (geometry)|solid]]s, [[vector]]s, [[surface (geometry)|surfaces]] and others in a space, such as [[plane]], a higher dimensional Euclidean space, a sphere or other [[non-Euclidean space]], or more generally, a [[manifold]]. | In common parlance, '''geometry''' is a branch of mathematics that studies the relationships between figures such as [[point (geometry)|points]], [[line (geometry)|lines]], [[polygon]]s, [[solid (geometry)|solid]]s, [[vector]]s, [[surface (geometry)|surfaces]] and others in a space, such as [[plane]], a higher dimensional Euclidean space, a sphere or other [[non-Euclidean space]], or more generally, a [[manifold]]. | ||
As a mathematical term, '''geometry''' refers to either the spatial ([[metric]]) properties of a given space or, more specifically in [[differential geometry]], a given complete locally homogeneous Riemannian manifold. | As a mathematical term, '''geometry''' refers to either the spatial ([[metric space|metric]]) properties of a given space or, more specifically in [[differential geometry]], a given complete locally homogeneous Riemannian manifold. | ||
==History of geometry== | ==History of geometry== | ||
The ancient Greeks developed the formal structure of geometry, including the use of mathematical [[proof]]s to demonstrate claims, and distinguishing between [[axiom]]s, definitions, and [[theorem]]s. [[Euclid]], a Greek mathematician living in [[Alexandria]] about 300 BC wrote a 13-volume book of geometry titled ''The Elements'' (''Στοιχεῖα''), which set forth in a structured way the geometrical knowledge of the Greeks. | The ancient Greeks developed the formal structure of geometry, including the use of mathematical [[proof]]s to demonstrate claims, and distinguishing between [[axiom]]s (and postulates), definitions, and [[theorem]]s. [[Euclid]], a Greek mathematician living in [[Alexandria]] about 300 BC wrote a 13-volume book of geometry titled ''The Elements'' (''Στοιχεῖα''), which set forth in a structured way the geometrical knowledge of the Greeks. | ||
Revision as of 03:52, 13 November 2007
In common parlance, geometry is a branch of mathematics that studies the relationships between figures such as points, lines, polygons, solids, vectors, surfaces and others in a space, such as plane, a higher dimensional Euclidean space, a sphere or other non-Euclidean space, or more generally, a manifold.
As a mathematical term, geometry refers to either the spatial (metric) properties of a given space or, more specifically in differential geometry, a given complete locally homogeneous Riemannian manifold.
History of geometry
The ancient Greeks developed the formal structure of geometry, including the use of mathematical proofs to demonstrate claims, and distinguishing between axioms (and postulates), definitions, and theorems. Euclid, a Greek mathematician living in Alexandria about 300 BC wrote a 13-volume book of geometry titled The Elements (Στοιχεῖα), which set forth in a structured way the geometrical knowledge of the Greeks.