Assume you are a superman who is very elastic, after making linked rings with your index fingers and thumbs, could you move your hands apart without separating the joined fingertips?

In other words, is it possible to go from (a) to (b) without “breaking” the figure above?

Figure taken from Intuitive Topology (Mathematical World, Vol 4).

The answer is yes!

This is an animation of the solution: https://vk.com/video-9666747_142799479

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That’s a nice counter-intuitive puzzle. Although the animated solution is a little creepier than I thought it would be! :’D

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Yeah the animation is kind of creepy 🙂

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An absorbing puzzle in itself. Also, becoz topology is rubber sheet geometry. In Topology, One studies those properties which are invariant under stretching, twisting, pulling, bending; and, finally cutting up and coalescing the same points. I think the specific question you have put forth is also in Intuitive Topology of Prasolov. May I also mention that there is a nice little booklet “Intuitive Concepts in Elementary Topology” by B H Arnold, which discusses these v fundamental geometric or ‘visual” aspects of topology by means of a number of examples and problems. It is a Dover Publication and hence, luckily, affordable to buy !!!

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Nice! I will check out the book by B H Arnold, thanks for the recommendation.

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