Stacks of Reflecting Plates

A ray of light enters a stack of glass plates. The ray can either pass through a plate or be reflected by it. This Demonstration shows all the possible ways the ray has to leave the stack after reflections. If is even, the ray traverses the stack, otherwise it leaves the stack on the same side it entered.
With plates, the surfaces are labeled , with denoting the lower surface of the lowest plate, and a ray with reflections is uniquely determined by surface labels.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


With two plates the number of paths with reflections is the Fibonacci number . With three plates the number of paths is for , which is Sloane's sequence A006356.
R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics, 2nd ed., Reading, MA: Addison-Wesley, 1994 p. 291.
Sequence A006356 in N. J. A. Sloane, ed., The On-Line Encyclopedia of Integer Sequences, 2008.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+