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  • Definition of music — How to define music has long been the subject of debate; philosophers, musicians, and, more recently, various social and natural scientists have argued about what constitutes music. The definition has varied through history, in different regions …   Wikipedia

  • History of geometry — Geometry (Greek γεωμετρία ; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre modern mathematics, the other being the study of numbers. Classic geometry… …   Wikipedia

  • Greek arithmetic, geometry and harmonics: Thales to Plato — Ian Mueller INTRODUCTION: PROCLUS’ HISTORY OF GEOMETRY In a famous passage in Book VII of the Republic starting at Socrates proposes to inquire about the studies (mathēmata) needed to train the young people who will become leaders of the ideal… …   History of philosophy

  • Coordinative definition — A coordinative definition is a postulate which assigns a partial meaning to the theoretical terms of a scientific theory by correlating the mathematical objects of the pure or formal/syntactical aspects of a theory with physical objects in the… …   Wikipedia

  • Motive (algebraic geometry) — For other uses, see Motive (disambiguation). In algebraic geometry, a motive (or sometimes motif, following French usage) denotes some essential part of an algebraic variety . To date, pure motives have been defined, while conjectural mixed… …   Wikipedia

  • Whitehead's point-free geometry — In mathematics, point free geometry is a geometry whose primitive ontological notion is region rather than point. Two axiomatic systems are set out below, one grounded in mereology, the other in mereotopology and known as connection theory… …   Wikipedia

  • Plane (geometry) — Two intersecting planes in three dimensional space In mathematics, a plane is a flat, two dimensional surface. A plane is the two dimensional analogue of a point (zero dimensions), a line (one dimension) and a space (three dimensions). Planes can …   Wikipedia

  • Continuous geometry — In mathematics, continuous geometry is an analogue of complex projective geometry introduced by von Neumann (1936, 1998), where instead of the dimension of a subspace being in a discrete set 0, 1, ..., n, it can be an element of the unit… …   Wikipedia

  • Euclidean geometry — A Greek mathematician performing a geometric construction with a compass, from The School of Athens by Raphael. Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his… …   Wikipedia

  • Projective geometry — is a non metrical form of geometry, notable for its principle of duality. Projective geometry grew out of the principles of perspective art established during the Renaissance period, and was first systematically developed by Desargues in the 17th …   Wikipedia

  • Birational geometry — In mathematics, birational geometry is a part of the subject of algebraic geometry, that deals with the geometry of an algebraic variety that is dependent only on its function field. In the case of dimension two, the birational geometry of… …   Wikipedia

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