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In number theory, the geometry of numbers studies convex bodies and integer vectors in n-dimensional space.〔MSC classification, 2010, available at http://www.ams.org/msc/msc2010.html, Classification 11HXX.〕 The geometry of numbers was initiated by . 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.〔Schmidt's books. Grötschel et alia, Lovász et alia, Lovász.〕 ==Minkowski's results== (詳細はlattice in ''n''-dimensional Euclidean space R''n'' and ''K'' is a convex centrally symmetric body. Minkowski's theorem, sometimes called Minkowski's first theorem, states that if , then ''K'' contains a nonzero vector in Γ. (詳細はinf of the numbers λ such that λ''K'' contains ''k'' linearly independent vectors of Γ. Minkowski's theorem on successive minima, sometimes called Minkowski's second theorem, is a strengthening of his first theorem and states that〔Cassels (1971) p.203〕 : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「geometry of numbers」の詳細全文を読む スポンサード リンク
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