Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in and the study of these lattices provides fundamental information on algebraic numbers.[1] The geometry of numbers was initiated by Hermann Minkowski (1910).
The geometry of numbers has a close relationship with other fields of mathematics, especially functional analysis and Diophantine approximation, the problem of finding rational numbers that approximate an irrational quantity.[2]
- ^ MSC classification, 2010, available at http://www.ams.org/msc/msc2010.html, Classification 11HXX.
- ^ Schmidt's books. Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419