Paper Mathematics - Part 3

Geometry Level 3

Above is an image of a left single half twist Möbius strip and a right single half twist Möbius strip glued together at right angles.

What shape do you get after you cut along the dashed lines?

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.

See Part 1 and Part 2.

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

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.