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Geometry of Continued Fractions (Hardcover, 2nd ed. 2022)
Loot Price: R2,144
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Geometry of Continued Fractions (Hardcover, 2nd ed. 2022)
Series: Algorithms and Computation in Mathematics, 26
Expected to ship within 12 - 17 working days
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This book introduces a new geometric vision of continued fractions.
It covers several applications to questions related to such areas
as Diophantine approximation, algebraic number theory, and toric
geometry. The second edition now includes a geometric approach to
Gauss Reduction Theory, classification of integer regular polygons
and some further new subjects. Traditionally a subject of number
theory, continued fractions appear in dynamical systems, algebraic
geometry, topology, and even celestial mechanics. The rise of
computational geometry has resulted in renewed interest in
multidimensional generalizations of continued fractions. Numerous
classical theorems have been extended to the multidimensional case,
casting light on phenomena in diverse areas of mathematics. The
reader will find an overview of current progress in the geometric
theory of multidimensional continued fractions accompanied by
currently open problems. Whenever possible, we illustrate geometric
constructions with figures and examples. Each chapter has exercises
useful for undergraduate or graduate courses.
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