Borromean rings

Geometry Level 2

The picture above is of the famous borromean rings . Is it physically possible to make this configuration?

Details and Assumptions :

  • All rings are rigid and the tube part of the rings are of finite thickness.
  • All rings are circular and can have either equal or differing radii.
No Nobody knows Yes

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Isaac Buckley by Isaac Buckley , 24, United Kingdom

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5 solutions

Achille 'Gilles'
Aug 2, 2015

The red ring cross twice the blue and is clearly under it. The green ring cross twice the blue and is clearly over it. How come the red could go under the blue, over the green and again under the blue? So this picture an impossible representation.

8 Helpful 0 Interesting 0 Brilliant 0 Confused
Keshav Bassi
Jul 31, 2015

This figure is only possible when the rings are not rigid i.e. they can be bend.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

It's also possible when the rings are not circular.

Isaac Buckley - 5 years, 10 months ago
Prabhav Bansal
Aug 7, 2015

it can be possible if we could break any one ring. Most probably blue one .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Well, we're not allowed to break the rings...

This problem is interesting because even though we can draw it, we cannot actually construct it in the physical world.

Hadia Qadir
Aug 2, 2015

The red ring cross twice the blue and is clearly under it. The green ring cross twice the blue and is clearly over it. How come the red could go under the blue, over the green and again under the blue? So this picture an impossible representation.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Timothy Wan
Jul 29, 2015

Rigid rings cannot make this configuration as the ring has to bend. This is seen from the contact points of the red ring to the blue and green rings.The red ring goes under-over-under,which cannot happen with a solid ring on all three rings.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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