9860

Deforming a Möbius Band with a Triangular Boundary

A Möbius band with triangular boundary was described by Tuckerman [1]. This Demonstration shows a translucent model of it with a dark, thick boundary line. You can continuously deform the boundary in the band until it doubly covers a central loop.

SNAPSHOTS

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

DETAILS

The Möbius band is the most well-known nonorientable surface. However, it is not as well-known that it has a nonsingular polyhedral embedding in Euclidean space with a triangular boundary. This embedding consists of six of the equilateral triangular faces from an octahedron and three interior right triangular pieces, one twice the size of the other two. We show how to continuously deform the boundary triangle in the Möbius band into a central loop, covering it twice. The snapshots show the starting position, an intermediate position, and nearly the final position, with the curve about to go over itself.
Reference
[1] B. Tuckerman, "A Non-Singular Polyhedral Möbius Band Whose Boundary Is a Triangle," The American Mathematical Monthly, 55(5), 1948 pp. 309–311. www.jstor.org/stable/2305482.
    • 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+