Philosophy

Pure mathematics

Boundary (topology)

Planar

Computer graphics (images)

Dynamical billiards

Computer science

Simple (philosophy)

Classical mechanics

Physics

Mathematics

Epistemology

Mathematical analysis

Differential geometry

Geometry

Periodic orbits

Parallelogram

Piecewise

Regular polygon

Hinge

Journal of Geometric Analysis

We give a simple proof of the result of Tumanov and Zharnitsky (Int Math Res Not, 2006) that the set of period 4 orbits in planar outer billiard with piecewise smooth convex boundary has empty interior, provided that no four corners of the boundary form a parallelogram. We also obtain results on period 5 and 6 orbits.

Scarcity of Periodic Orbits in Outer Billiards