Geometry of continued fractions /
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 th...
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| Müşterek Yazar: | |
| Materyal Türü: | Ekitap |
| Dil: | English |
| Baskı/Yayın Bilgisi: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2013.
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| Seri Bilgileri: | Algorithms and Computation in Mathematics
26 |
| Konular: | |
| Online Erişim: | Click here to view the full text content |
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| Özet: | 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. 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 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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| Fiziksel Özellikler: | 1 online resource (XVII, 405 pages) 114 illustrations. digital |
| ISBN: | 9783642393686 |
| ISSN: | 1431-1550 |