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geometry of numbers

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  • Geometry of numbers — In number theory, the geometry of numbers is a topic and method arising from the work of Hermann Minkowski, on the relationship between convex sets and lattices in n dimensional space. It has frequently been used in an auxiliary role in proofs,… …   Wikipedia

  • Geometry — (Greek γεωμετρία ; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences. Initially a body of… …   Wikipedia

  • geometry — /jee om i tree/, n. 1. the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties… …   Universalium

  • geometry — Although various laws concerning lines and angles were known to the Egyptians and the Pythagoreans, the systematic treatment of geometry by the axiomatic method began with the Elements of Euclid . From a small number of explicit axioms,… …   Philosophy dictionary

  • Complex analytic geometry — In mathematics, complex analytic geometry sometimes denotes the application of complex numbers to plane geometry. Rather than represent a point in the plane as a pair of Cartesian coordinates, it can be represented as a single complex number,… …   Wikipedia

  • List of geometry topics — This is list of geometry topics, by Wikipedia page.*Geometric shape covers standard terms for plane shapes *List of mathematical shapes covers all dimensions *List of differential geometry topics *List of geometers *See also list of curves, list… …   Wikipedia

  • Discrete geometry — A collection of circles and the corresponding unit disk graph Combinatorial geometry redirects here. The term combinatorial geometry is also used in the theory of matroids to refer to a simple matroid, especially in older texts. Discrete geometry …   Wikipedia

  • Convex geometry — is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral… …   Wikipedia

  • Systolic geometry — In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner, and developed by Mikhail Gromov and others, in its arithmetic, ergodic, and topological manifestations.… …   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

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