# Semi-Annular Spiral Billiard with Periodic Orbits

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows spiral-shaped billiard tables patched together using annular pieces. Starting at zero radians on the positive axis, and repeating every radians counter-clockwise around the spiral, periodic orbits occur where tangents to a table's inner and outer curved boundaries are parallel for the same spiral angle. To construct a table, users can choose the number of loops around the spiral and the rate at which the width of the spiral increases.

[more]
Contributed by: William C. Hill (March 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The trajectory calculations are based on figure 1 on page 539 of [1].

Reference

[1] J. S. Espinoza Ortiz and R. Egydio de Carvalho, "Energy Spectrum and Eigenfunctions through the Quantum Section Method," *Brazilian Journal of Physics*, 31(4), 2001 pp. 538–545.

## Permanent Citation