Topology Puzzle

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?

Screen Shot 2016-04-07 at 6.14.36 PM

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:

Author: mathtuition88

Math and Education Blog

5 thoughts on “Topology Puzzle”

  1. 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 !!!

    Liked by 1 person

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