All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Linked Rings (Posted on 2004-05-29) Difficulty: 2 of 5
Three rings (planar circles) are "linked" together, but you'll notice that none is directly linked with another.
  • The red ring is "behind" the yellow.
  • The yellow ring is "behind" the blue.
  • The blue ring is "behind" the red.
Still, while none is intertwined with another, it is impossible to pull them apart.

Is this a paradox?

Can this really be built?

No Solution Yet Submitted by SilverKnight    
Rating: 3.6000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Make mine a Borromean Ale. | Comment 8 of 19 |
This shape is very much possible to make in 3 dimensions but not with rigid circular rings.

I used to make it all the time with 3 soda straws. The key with straws is to make the rings triangular or rectangular.

I can attempt to describe how to make a drawing to show how this works:

Draw a 3-D Cartesian graph. Draw three 2x4 rectangles with coordinates as follows:
(2,1,0) (2,-1,0) (-2,-1,0) (-2,1,0)
(0,2,1) (0,2,-1) (0,-2,-1) (0,-2,1)
(1,0,2) (1,0,-2) (-1,0,-2) (-1,0,2)
If you draw these rectangles first lightly, then darkening the parts in the front you can see the pattern. No two of them are actually linked at all, yet the third keeps them together.

  Posted by Jer on 2004-05-29 16:07:19
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information