Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 22, No. 3, pp. 217-235 (2006)

Linkages between the Gauss Map and the Stern-Brocot Tree

Bruce Bates, Martin Bunder, Keith Tognetti

University of Wollongong

Abstract: We discover a bijective map between the Gauss Map and the left-half of the Stern-Brocot Tree. The domain of the Gauss Map is then extended to cover all reals, and the coverage of the Stern-Brocot Tree is extended to include all positive and negative rationals in a manner that preserves the map between the two constructions.

Keywords: Gauss Map, Stern-Brocot Tree.

Classification (MSC2000): 11A55; 05C05

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