If you like topology, this one is really fantastic.

If you like topology, this one is really fantastic. I don't want to spoil the progression, but let me just say the amount of glasswork is surprising. Gotta love Cliff!

Originally shared by Numberphile

Extras for this video: https://youtu.be/6Qpfv5y-7WU

More Cliff: http://bit.ly/Cliff_Videos
https://www.youtube.com/watch?v=k8Rxep2Mkp8&feature=autoshare

Comments

  1. Melinda GreenSeptember 9, 2016 at 12:09 AM

    Yea, I paused on the initial sketch, made my bet and got the right answer! I didn't do it the way he did though. Spoiler alert! I realized that it's perfectly fine to pass one tube through any other, because this is a problem of surfaces, not knots. So the fact that one tube initially dives straight through a ring within another tube doesn't trap it in any way. His solution elegantly side-steps that intersection but topologically it's unnecessary and the result is the same.

    ReplyDelete
  2. Roice NelsonSeptember 9, 2016 at 7:39 AM

    Nice, I wish I would have tested myself like that! And I like your observation, which would have enhanced the video if it had been mentioned.

    I wrote Cliff yesterday to see if he will be selling any of these, like his Klein bottles. I want the model of the sphere with 3 handles :)

    ReplyDelete
  3. Arnaud ChéritatSeptember 14, 2016 at 11:13 AM

    Thanks for the link. Amazing work. And I did not expect you could do it /without/ crossing.

    ReplyDelete

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