Wolfram Demonstrations Project

12,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Paradoxical Triangular Braid

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This triangular braid with three links colored red, yellow, and blue was designed by Koos Verhoeff and realized as mathematical art in three types of wood. The paradox comes about as follows. If there is no red link, then the blue link is completely on top of the yellow link. If there is no yellow link, then the red is completely on top of the blue. Finally, if there is no blue link, then the yellow link is completely on top of the red. How can it be that yellow is above red, red is above blue, and blue is above yellow?

[more]

In topology, a knot is an embedding of a circle in 3D (with no loose ends). A link is a collection of knots that may be intertwined.

This arrangement is an example of a Brunnian link, which cannot be taken apart without cutting a link, but when one link is removed, the others come apart without cutting. The Borromean rings are the simplest Brunnian links.

[less]

Contributed by: Tom Verhoeff  (August 2013)
(Eindhoven University of Technology)
Open content licensed under CC BY-NC-SA

Snapshots

Details

See [1] for details on the design of this triangular braid. For a video, see http://www.youtube.com/watch?v=3b_P9TPnxGA.

Reference

[1] T. Verhoeff, "3D Turtle Geometry: Artwork, Theory, Program Equivalence and Symmetry," International Journal of Arts and Technology, 3(2/3), 2010 pp. 288–319.

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send