9873

Fault-Free Tilings

A tiling is called fault free if it has no "breaking line" (a straight line that does not go through the interior of any tile).
In this Demonstration you are asked to create a few fault-free tilings using copies of a single tile.

THINGS TO TRY

SNAPSHOTS

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

DETAILS

To place a tile, move the sample to the position you want, then use the slider for the proper rotation, and finally click the "store new tile" button.
The first three examples in this Demonstration deal with the problem of packing rectangles into a rectangular box. In 1980 the author showed (in the Journal of Recreational Mathematics) that the ( box is the smallest box that allows a fault-free packing of tiles.
The author also showed how in general a ( box can be packed with tiles, and he conjectured that this is indeed the smallest box of this type for any numbers and with no common divisor. This interesting result answered a question posed by Martin Gardner.
Example 4 is taken from the author's book A Puzzling Journey to the Reptiles and Related Animals, 1987, published privately.
Reference: M. Gardner, New Mathematical Diversions from Scientific American, New York: Simon and Schuster, 1966.
    • 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.









 
RELATED RESOURCES
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 © 2014 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+