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## Obtuse Triangular Billiards II: 100 Degrees Worth of Periodic Trajectories

Citations: | 9 - 1 self |

### Citations

833 | Mathematica: A System for Doing Mathematics by Computer - Wolfram - 1991 |

135 |
Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
- Veech
- 1989
(Show Context)
Citation Context ...rd paths [BGKT]. (See also [M].) There has been a lot of interest in rational billiards lately, owing to the deep connections it has to many areas of mathematics, such as Teichmuller theory; see e.g. =-=[V]-=- or the surveys mentioned above. In [GSV] and [HH], some infinite families of periodic orbits, which work for some obtuse irrational triangles, are produced. Aside from these results, very little is k... |

48 |
Billiards in polygons: Survey of recent results
- Gutkin
- 1996
(Show Context)
Citation Context ... T , composed of line segments, such that each vertex si ∩ si+1 lies in the interior of some edge of T , say the with edge, and the angles that si and si+1 make with this edge are complementary. (See =-=[G]-=-, [MT] and [T] for surveys on billiards.) The sequence {wi} is the orbit type. In 1775 Fagnano proved that the combinatorial orbit 123 (repeating) describes a periodic orbit on every acute triangle. I... |

47 |
Closed trajectories for quadratic differentials with an application to billiards
- Masur
- 1986
(Show Context)
Citation Context ...ggenheim Fellowship, and by the Ruth M. Davis Endowment. 1 rational triangle−i.e. a triangle whose angles are all rational multiples of pi−has a dense set of periodic billiard paths [BGKT]. (See also =-=[M]-=-.) There has been a lot of interest in rational billiards lately, owing to the deep connections it has to many areas of mathematics, such as Teichmuller theory; see e.g. [V] or the surveys mentioned a... |

10 |
On periodic billiard trajectories in obtuse triangles
- Halbeisen, Hungerbühler
(Show Context)
Citation Context ... lot of interest in rational billiards lately, owing to the deep connections it has to many areas of mathematics, such as Teichmuller theory; see e.g. [V] or the surveys mentioned above. In [GSV] and =-=[HH]-=-, some infinite families of periodic orbits, which work for some obtuse irrational triangles, are produced. Aside from these results, very little is known about the obtuse (irrational) case of triangu... |

6 |
Periodic billiard paths in right triangles are unstable,” Geometriae Dedicata
- Hooper
- 2007
(Show Context)
Citation Context ...ombinatorial orbit 123 (repeating) describes a periodic orbit on every acute triangle. It is an exercise to show that 312321 (repeating) describes a periodic orbit on all right triangles. (See [GSV], =-=[H]-=-, and [Tr] for some deeper results on right angled billiards.) A ∗ This research is supported by N.S.F. Grant DMS-0305047, by a Guggenheim Fellowship, and by the Ruth M. Davis Endowment. 1 rational tr... |

2 |
Periodic Billiard Trajectories are Dense
- Boshernitzyn, Galperin, et al.
- 1998
(Show Context)
Citation Context ...S-0305047, by a Guggenheim Fellowship, and by the Ruth M. Davis Endowment. 1 rational triangle−i.e. a triangle whose angles are all rational multiples of pi−has a dense set of periodic billiard paths =-=[BGKT]-=-. (See also [M].) There has been a lot of interest in rational billiards lately, owing to the deep connections it has to many areas of mathematics, such as Teichmuller theory; see e.g. [V] or the surv... |

1 |
Obtuse Triangular Billiards I: Near the (2
- Schwartz
- 2006
(Show Context)
Citation Context ...S, we only need 5 of these tiles to cover S ∩ P4. • It seems that no neighborhood of p5 can be covered by a single orbit tile. However, we will cover a neighborhood P5 of p5 using 2 orbit tiles. • In =-=[S1]-=- we proved that no neighborhood of p6 can be covered by finitely many orbit tiles. However, in [S1] we covered a tiny neighborhood P6 of p6 using infinitely many orbit tiles. We will use this result h... |