Linking and Unlinking a Double Torus.

March 12, 2011

I cannot find a suitable picture of a linked double torus, which makes me think it’s called something else.   Luckily, because it’s on the cover of Armstrong’s book (and I don’t think Springer would mind some free advertising) we can reproduce it here:

image

Now, how can we take this "linked" double torus and make it an "unlinked" double torus without cutting anything up?  This one kept me up last night, but the solution turns out to be quite easy once you see it. 

If you don’t want the full solution, a hint might be: start thinking of the double torus as two handles on a sphere.  What can you do with these handles?

 

The picture solution after the jump.

FxCam_1299912423259

Click to make this bigger.

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3 Responses to “Linking and Unlinking a Double Torus.”

  1. Daniel said

    I saw that question in the book a while back and had no idea how to solve it. I even thought intuitively that there was no way to separate them.

    It is quite a counter-intuitive thing.

  2. Linda said

    I still can’t wrap my mind around it. I need to see it. It almost reminds me of that metal brainteaser.

  3. Tom said

    Hey I got it! That hint made all the difference.

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