Diophantine approximation: Difference between revisions

Revision as of 23:52, 28 November 2021

Revision as of 00:43, 28 December 2021

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===Lagrange spectrum ===

{{main|Markov spectrum}}

As said above, the constant in Borel's theorem may not be improved, as shown by [[Adolf Hurwitz]] in 1891.<ref>{{harvnb|Hardy|Wright|1979|p=164}}</ref>

Let <math>\phi = \tfrac{1+\sqrt{5}}{2}</math> be the [[golden ratio]].

Then for any real constant ''c'' with <math>c > \sqrt{5}\;</math> there are only a finite number of rational numbers {{math|''p''/''q''}} such that