Geometry of numbers

Geometry of numbers is the part of <a href="/facts/Number_theory/zhoa7zrc">number theory</a> which uses <a href="/facts/Geometry/wTQf5ffQ">geometry</a> for the study of <a href="/facts/Algebraic_number/MkH1PzTK">algebraic numbers</a>. Typically, a <a href="/facts/Ring_of_algebraic_integers/Qb0fD3R3">ring of algebraic integers</a> is viewed as a <a href="/facts/Lattice_(group)/2ls9Iv9N">lattice</a> in 
 
 
 
 
 
 R
 
 
 n
 
 
 ,
 
 
 {\displaystyle \mathbb {R} ^{n},}
 
 and the study of these lattices provides fundamental information on algebraic numbers. <a href="/facts/Hermann_Minkowski/tlKrpw69">Hermann Minkowski</a> (1896) initiated this line of research at the age of 26 in his work The Geometry of Numbers.

The geometry of numbers has a close relationship with other fields of mathematics, especially <a href="/facts/Functional_analysis/MIp233MT">functional analysis</a> and <a href="/facts/Diophantine_approximation/WGVMuWF4">Diophantine approximation</a>, the problem of finding <a href="/facts/Rational_number/VJQmyY05">rational numbers</a> that approximate an <a href="/facts/Irrational_number/Psv19TET">irrational quantity</a>.

Geometry of numbers open-in-new

Geometry of numbers