Archiv der Mathematik

, Volume 105, Issue 2, pp 129–137 | Cite as

Sharpening of theorems of Vahlen and Hurwitz and approximation properties of the golden ratio

  • Jaroslav Hančl


We improve the well-known theorems of Hurwitz and Vahlen from Diophantine approximation theory and give the proof that the numbers golden ratio and reciprocal one plus golden ratio have some exeptional properties in approximation of irrational real numbers by rationals.

Mathematics Subject Classification

Primary 11J82 Secondary 11A55 


Continued fraction Approximation Golden ratio 


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Authors and Affiliations

  1. 1.Division of UO, Department of Mathematics, Centre of Excellence IT4Innovation, Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaOstrava 1Czech Republic

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