Editing Geometry of numbers (section)

{{Short description|Application of geometry in number theory}}
'''Geometry of numbers''' is the part of [[number theory]] which uses [[geometry]] for the study of [[algebraic number]]s. Typically, a [[ring of algebraic integers]] is viewed as a [[lattice (group)|lattice]] in <math>\mathbb R^n,</math> and the study of these lattices provides fundamental information on algebraic numbers.<ref>MSC classification, 2010, available at http://www.ams.org/msc/msc2010.html, Classification 11HXX.</ref>  {{harvs|txt|authorlink=Hermann Minkowski|first=Hermann|last= Minkowski|year=1896|ref1=https://mathweb.ucsd.edu/~b3tran/cgm/Minkowski_SpaceAndTime_1909.pdf}} initiated this line of research at the age of 26 in his work ''The Geometry of Numbers''.<ref>{{Cite book |last=Minkowski |first=Hermann |url=https://books.google.com/books?id=D-J9AgAAQBAJ&dq=Space+and+Time+Minkowski%E2%80%99s+Papers+on+Relativity&pg=PA1 |title=Space and Time: Minkowski's papers on relativity |date=2013-08-27 |publisher=Minkowski Institute Press |isbn=978-0-9879871-1-2 |language=en}}</ref>

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The geometry of numbers has a close relationship with other fields of mathematics, especially [[functional analysis]] and [[Diophantine approximation]], the problem of finding [[rational number]]s <!-- or vectors with rational coordinates SIMPLIFY --> that <!-- accurately --> approximate an [[irrational number|irrational quantity]].<ref>Schmidt's books. {{Cite Geometric Algorithms and Combinatorial Optimization}}</ref>