What does analytic geometry mean?

Definitions for analytic geometry
an·a·lyt·ic ge·om·e·t·ry

This dictionary definitions page includes all the possible meanings, example usage and translations of the word analytic geometry.

Princeton's WordNet

  1. analytic geometry, analytical geometry, coordinate geometrynoun

    the use of algebra to study geometric properties; operates on symbols defined in a coordinate system

Wiktionary

  1. analytic geometrynoun

    a branch of mathematics that investigates properties of figures through the coordinates of their points.

Wikipedia

  1. Analytic geometry

    In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.

ChatGPT

  1. analytic geometry

    Analytic geometry, also known as coordinate geometry or Cartesian geometry, is a branch of mathematics that uses algebraic equations to describe the size, position, and shape of geometric figures on a coordinate system. This field of study establishes a direct connection between geometry and algebra by using numbers and variables to represent geometric concepts. It allows for the solution of geometric problems through numerical and algebraic calculations, and for the representation of geometric figures in a real number coordinate system. The foundational work in this discipline was laid down by French mathematician Rene Descartes and his contemporaries in the 17th century.

Wikidata

  1. Analytic geometry

    Analytic geometry, or analytical geometry, has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning. In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis. This contrasts with the synthetic approach of Euclidean geometry, which treats certain geometric notions as primitive, and uses deductive reasoning based on axioms and theorems to derive truth. Analytic geometry is widely used in physics and engineering, and is the foundation of most modern fields of geometry, including algebraic, differential, discrete, and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. The numerical output, however, might also be a vector or a shape. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.

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How to pronounce analytic geometry?

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Numerology

  1. Chaldean Numerology

    The numerical value of analytic geometry in Chaldean Numerology is: 5

  2. Pythagorean Numerology

    The numerical value of analytic geometry in Pythagorean Numerology is: 4


Translations for analytic geometry

From our Multilingual Translation Dictionary

  • geometría analíticaSpanish
  • analitikus geometriaHungarian
  • geometria analiticaItalian
  • аналитичка геометријаMacedonian
  • аналити́ческая геоме́трияRussian
  • analytisk geometriSwedish
  • பகுப்பாய்வு வடிவியல்Tamil
  • analitik geometriTurkish

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"analytic geometry." Definitions.net. STANDS4 LLC, 2024. Web. 28 Mar. 2024. <https://www.definitions.net/definition/analytic+geometry>.

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