The plaid model:
Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary bill...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton and Oxford
Princeton University Press
2019
|
| Schriftenreihe: | Annals of mathematics studies
Number 198 |
| Schlagworte: | |
| Online-Zugang: | FHR51 UBW01 UBY01 Volltext |
| Zusammenfassung: | Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a self-contained sequel to Richard Schwartz’s Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites.Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called "the plaid model," has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics.The book includes an extensive computer program that allows readers to explore materials interactively and each theorem is accompanied by a computer demo |
| Beschreibung: | 1 Online-Ressource (xii, 268 Seiten) Illustrationen, Diagramme |
| ISBN: | 9780691188997 |
| DOI: | 10.1515/9780691188997 |
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Datensatz im Suchindex
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| author | Schwartz, Richard Evan 1966- |
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| discipline | Mathematik |
| doi_str_mv | 10.1515/9780691188997 |
| format | Electronic eBook |
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| id | DE-604.BV045920588 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:30:22Z |
| institution | BVB |
| isbn | 9780691188997 |
| language | English |
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| series | Annals of mathematics studies |
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| spelling | Schwartz, Richard Evan 1966- Verfasser (DE-588)102219111X aut The plaid model Richard Evan Schwartz Princeton and Oxford Princeton University Press 2019 1 Online-Ressource (xii, 268 Seiten) Illustrationen, Diagramme txt rdacontent c rdamedia cr rdacarrier Annals of mathematics studies Number 198 Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a self-contained sequel to Richard Schwartz’s Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites.Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called "the plaid model," has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics.The book includes an extensive computer program that allows readers to explore materials interactively and each theorem is accompanied by a computer demo Astronomie (DE-588)4003311-9 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Astronomie (DE-588)4003311-9 s Dynamisches System (DE-588)4013396-5 s DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-0-691-18137-0 Erscheint auch als Druck-Ausgabe, Paperback 978-0-691-18138-7 Annals of mathematics studies Number 198 (DE-604)BV040389493 198 https://doi.org/10.1515/9780691188997 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Schwartz, Richard Evan 1966- The plaid model Annals of mathematics studies Astronomie (DE-588)4003311-9 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4003311-9 (DE-588)4013396-5 |
| title | The plaid model |
| title_auth | The plaid model |
| title_exact_search | The plaid model |
| title_full | The plaid model Richard Evan Schwartz |
| title_fullStr | The plaid model Richard Evan Schwartz |
| title_full_unstemmed | The plaid model Richard Evan Schwartz |
| title_short | The plaid model |
| title_sort | the plaid model |
| topic | Astronomie (DE-588)4003311-9 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Astronomie Dynamisches System |
| url | https://doi.org/10.1515/9780691188997 |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT schwartzrichardevan theplaidmodel |