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Exercise 1.4 on Saveliev "Illustrated Topology" gives a picture of locked hands and asks how can we unlock them without breaking the loops. I've thought about it and couldn't find a way. I'd appreciate a hint. Is it even possible? locked hands

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    $\begingroup$ One way is to move the place where the purple thumb is attached to the body - along the purple arm, then along the chest, then along the green arm, then let it go though the loop formed by the green thumb and index, and finally return along the green arm etc to where it was originally. (This description might be difficult to understand without an cartoon :) $\endgroup$
    – user8268
    Commented Aug 16, 2023 at 18:35
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    $\begingroup$ @user8268 it's difficult to understand with a cartoon :) . Would you mind expounding your answer? $\endgroup$ Commented Aug 16, 2023 at 20:18

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This is a classic. Before seeing the solution below note that this problem is equivalent to deforming (a) ↔ (b): enter image description here I you still have trouble imagining it, I highly recommend using e.g. salt dough and playing with it.

Solution:

enter image description here

Both figures are from the first pages of Prasolov, V. Intuitive Topology. Translated by A. Sossinsky. Vol. 4. Mathematical World. Providence, Rhode Island: American Mathematical Society, 1994. https://doi.org/10.1090/mawrld/004.

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  • $\begingroup$ Do you know if this is on youtube, by any chance? I'm still having trouble understanding this. $\endgroup$ Commented Aug 17, 2023 at 11:59
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    $\begingroup$ @DavidRaveh I am not aware of any animation or demonstration. I really recommend playing with salt dough (flour, salt + water), it will be more satisfying than seeing the answer. $\endgroup$
    – Kamil
    Commented Aug 17, 2023 at 12:59
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    $\begingroup$ I ended up taking your advice (I'm typing this with sticky fingers), and I get it now. I am having a hard time taking pictures of my solution, but thanks for your help. $\endgroup$ Commented Aug 17, 2023 at 15:38
  • $\begingroup$ @DavidRaveh Nice : ). You're welcome. $\endgroup$
    – Kamil
    Commented Aug 17, 2023 at 15:51

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