Paper mathematics - part 2

Geometry Level 3

Above is an image of regular loops joined together at right angles.

What shape do we get after cutting along the dashed lines?

Details and Assumptions :

  1. A half twist is a 18 0 180^{\circ} rotation of one side of the paper before you stick them together.

  2. We define a twisted loop to be a loop with a positive even number of half twists.


See Part 1 and Part 3 .

A single Möbius strip with a knot Two Möbius strips which are linked together Two Möbius strips which are seperate A single twisted loop with a knot Two twisted loops which are linked together A single twisted loop with no knot Two love hearts joined together A square

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1 solution

Isaac Buckley
Jan 15, 2016

square square

Yep, looks square to me.

I saw this on that Numberphile video on YouTube!

Adrian Castro - 5 years, 5 months ago

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I didn't know this was on Numberphile, what about part 1 and part 3?

Isaac Buckley - 5 years, 5 months ago

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Yeah this guy(forgot his name ) goes over them in a three part series called Unexpected Shapes. They're pretty cool, worth checking out.

Adrian Castro - 5 years, 5 months ago

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@Adrian Castro Thanks for informing me, I will check it out now.

Isaac Buckley - 5 years, 5 months ago

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@Isaac Buckley I didn't see part 1 on numberphile, although part 2 and 3 sadly are. Least I can teach people 1 thing that's new.

Isaac Buckley - 5 years, 5 months ago

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