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...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton ; NJ
Princeton University Press
[2019]
|
| Schriftenreihe: | Annals of mathematics studies
Number 198 |
| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 TUM01 UPA01 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 (xi, 267 Seiten |
| ISBN: | 9780691188997 |
| DOI: | 10.1515/9780691188997 |
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| discipline | Mathematik |
| doi_str_mv | 10.1515/9780691188997 |
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| id | DE-604.BV045924412 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:30:28Z |
| institution | BVB |
| isbn | 9780691188997 |
| language | English |
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| spelling | Schwartz, Richard Evan 1966- (DE-588)102219111X aut The Plaid model Richard Evan Schwartz Princeton ; NJ Princeton University Press [2019] © 2019 1 Online-Ressource (xi, 267 Seiten 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 In English MATHEMATICS / Geometry / General bisacsh Combinatorial dynamics Geometry Number theory Dynamisches System (DE-588)4013396-5 gnd rswk-swf Astronomie (DE-588)4003311-9 gnd rswk-swf Astronomie (DE-588)4003311-9 s Dynamisches System (DE-588)4013396-5 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-691-18137-0 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 MATHEMATICS / Geometry / General bisacsh Combinatorial dynamics Geometry Number theory Dynamisches System (DE-588)4013396-5 gnd Astronomie (DE-588)4003311-9 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4003311-9 |
| 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 | MATHEMATICS / Geometry / General bisacsh Combinatorial dynamics Geometry Number theory Dynamisches System (DE-588)4013396-5 gnd Astronomie (DE-588)4003311-9 gnd |
| topic_facet | MATHEMATICS / Geometry / General Combinatorial dynamics Geometry Number theory Dynamisches System Astronomie |
| url | https://doi.org/10.1515/9780691188997 |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT schwartzrichardevan theplaidmodel |