Hurwitz's theorem (number theory)
GPTKB entity
Statements (15)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
irrational real numbers
|
| gptkbp:concerns |
gptkb:Diophantine_approximation
|
| gptkbp:field |
number theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hurwitz's theorem (number theory)
|
| gptkbp:implies |
the best possible constant in the inequality is 1/√5.
|
| gptkbp:namedAfter |
gptkb:Adolf_Hurwitz
|
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:relatedTo |
gptkb:Dirichlet's_approximation_theorem
gptkb:Markov_numbers continued fractions |
| gptkbp:state |
For any irrational real number x, there are infinitely many rational numbers p/q such that |x - p/q| < 1/(√5 q^2).
|
| gptkbp:year |
1891
|
| gptkbp:bfsParent |
gptkb:Hurwitz's_theorem
|
| gptkbp:bfsLayer |
7
|