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:

A half twist is a \(180^{\circ}\) rotation of one side of the paper before you stick them together.
We define a twisted loop to be a loop with a positive even number of half twists.

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

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