Farey nets and multidimensional continued fractions

DOI10.1007/BF01572079zbMath0765.11029MaRDI QIDQ1207666

David J. Grabiner

Publication date: 12 May 1993

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178572

zbMATH Keywords

triangulationFarey sequencemultidimensional continued fractionFarey netMönkemeyer's algorithm

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Simultaneous homogeneous approximation, linear forms (11J13) Irrationality; linear independence over a field (11J72)

Related Items (8)

Triangles in Diophantine approximation ⋮ Simplex-karyon algorithm of multidimensional continued fraction expansion ⋮ Moments for the multidimensional Mönkemeyer algorithm ⋮ Multidimensional continued fractions and a Minkowski function ⋮ Linear-fractional invariance of the simplex-module algorithm for expanding algebraic numbers in multidimensional continued fractions ⋮ Asymptotics for two-dimensional Farey-Brocot nets ⋮ The n-dimensional Stern–Brocot tree ⋮ A two-dimensional Minkowski \(?(x)\) function

Cites Work

• Generalization of the Euclidean algorithm for real numbers to all dimensions higher than two
• Geodesic Multidimensional Continued Fractions
• Farey Triangles and Farey Quadrangels in the Complex Plane.
• Über die Struktur n-dimensionaler Fareynetze.
• Über Fareynetze in n Dimensionen
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