Outer Billiard - Open Questions

Open Questions

Outer billiards is a subject still in its beginning phase. Most problems are still unsolved. Here are some open problems in the area.

  • Show that outer billiards relative to almost every convex polygon has unbounded orbits.
  • Show that outer billiards relative to a regular polygon has almost every orbit periodic. The cases of the equilaterial triangle and the square are trivial, and Tabachnikov answered this for the regular pentagon. These are the only cases known.
  • more broadly, characterize the structure of the set of periodic orbits relative to the typical convex polygon.
  • understand the structure of periodic orbits relative to simple shapes in the hyperbolic plane, such as small equilateral triangles.

Read more about this topic:  Outer Billiard

Famous quotes containing the words open and/or questions:

    “The republican is the only form of government which is not eternally at open or secret war with the rights of mankind.”
    —Thomas Jefferson (1743–1826)

    “All questions rely on the present for their solution. Time measures nothing but itself. The word that is written may be postponed, but not that on the lip. If this is what the occasion says, let the occasion say it.”
    —Henry David Thoreau (1817–1862)