The Davenport-Schmidt theorem, named for Harold Davenport and Wolfgang M. Schmidt, is a result in the number-theory area of Diophantine approximation. It describes how well a certain kind of real number can be approximated by another kind, showing that irrational numbers which are not themselves quadratic can be well approximated using either quadratic irrationals or simple rational numbers. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementWe can get a good approximation to irrational numbers that are not quadratic by using either quadratic irrationals or simply rational numbers. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Source Davenport-Schmidt theorem (Wikipedia)
Sources
1. Davenport-Schmidt theorem (Wikipedia)
Introduction
we can get a good approximation to irrational numbers that are not quadratic by using either quadratic irrationals or simply rational numbers
In Branch: Number Theory, Lead section
In mathematics, specifically the area of Diophantine approximation, the Davenport-Schmidt theorem tells us how well
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