Paper Mathematics - Part 1

Geometry Level 4

Above is an image of a Möbius strip with three half twists.

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

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 2 and Part 3 .

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

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Isaac Buckley by Isaac Buckley , 24, United Kingdom

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1 solution

Isaac Buckley
Jan 15, 2016

knot knot

How do I know it's a twisted loop and not a Möbius strip (without cutting it, drawing on it or running my finger along it)?

What type of knot does it make?

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