World Library  
Flag as Inappropriate
Email this Article

Illumination problem

Article Id: WHEBN0030115275
Reproduction Date:

Title: Illumination problem  
Author: World Heritage Encyclopedia
Language: English
Subject: List of Numbers episodes (season 4), Roger Penrose
Publisher: World Heritage Encyclopedia

Illumination problem

Roger Penrose's solution of the illumination problem using elliptical arcs (blue) and straight line segments (green), with 3 positions of the single light source (red spot). The purple crosses are the foci of the larger arcs. Lit and unlit regions are shown in yellow and grey, respectively.

The illumination problem is a resolved mathematical problem first posed by Ernst Straus in the 1950s.[1] Straus asked if a room with mirrored walls can always be illuminated by a single point light source, allowing for repeated reflection of light off the mirrored walls. Alternatively, the question can be stated as asking that if a billiard table can be constructed in any required shape, is there a shape possible such that there is a point where it is impossible to the billiard ball in a at another point, assuming the ball is point-like and continues infinitely rather than stopping due to friction.

The problem was first solved in 1958 by [2] This was a borderline case, however, since a finite number of dark points (rather than regions) are unilluminable from any given position of the point source. An improved solution was put forward by D. Castro in 1997, with a 24-sided room with the same properties.[1]

Solutions to the illumination problem by George W Tokarsky (26 sides) and D Castro (24 sides).


  1. ^ a b c
  2. ^
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.