9758

Tiles with Finite Convex Spectra

Rearrange the given tiles to create convex shapes.
If copies of a tile can be arranged to form a convex shape without gaps or overlapping, then is said to belong to the "convex spectrum" of . The mathematical problem is to find all shapes with finite convex spectrum.
Since the tiles and convex spectra are already given in this Demonstration, all you have to do is to rearrange the given tiles. For example, if the convex spectrum is , one task is to arrange 3 tiles into a convex shape; another task is to arrange 6 tiles into a convex shape.

THINGS TO TRY

SNAPSHOTS

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

DETAILS

The problem of convex spectra was originally researched by Erich Friedman, Mike Reid, and the author of this Demonstration in 1999.
The term "convex spectrum" was introduced by Eric Friedman in 1999.
For example, the convex spectrum of a circle is {1}.
The convex spectrum of a half-circle is {1,2}.
This Demonstration considers the mathematical problem of finding all two-dimensional tiles with a finite convex spectrum.
Two interesting examples of tiles with an infinite convex spectrum are also included.
List of convex spectra displayed in this Demonstration:
    • 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 Curriculum Standards



 
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+