Möbius Strips

The Möbius strip, also called the ‘twisted cylinder,’ is a one-sided non-orientable surface, which means that the inside and outside are indistinguishable from each other. It is not technically a true surface, but rather a surface with boundary, due to the fact that its edges are non-distinct.

Fun Facts:

1. Möbius strips have many real-world applications, such as conveyor belts that last longer due to more distributed wear and typewriter ribbons that allow twice as much surface area to be covered in ink. You can also see these in fashion with infinity scarves.

2. The Möbius strip was first described by German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858, though images of a similar shape have been found in roman mosaics from 200 AD.

Terms to know

Topology – the branch of geometry that explore aspects
of shapes not connected to their measurements. Whereas conventional geometry focuses on length, area, volume, and angles, topology explores curvature, connections, and networks.

Möbius Strip – a surface with a single continuous surface and a single continuous edge.

Klein Bottle – a surface with a single continuous surface and no edges

Dimension – a measurable distance such as length, width, or height

Surface – an area with a length and width regardless of curving, bending, and folding

Boundary – the edge of a surface where it ends

Supplies

- Paper

- Scissors

- Marker, Pen, Pencil, Colored Pencil, or Crayon

- Scotch Tape

- Ruler

Step 1: Cut 1inch (2.5 Cm) Wide Strips of Paper at Least 8 Inches (20 Cm) Long.

Step 2: Tape One Side of the Paper to the Other to Make a Simple Loop.

Step 3: Draw a Line on the Inside of the Loop and One on the Outside.

Step 4: Cut Along the Line. You Will End Up With Two Separate Loops.

Step 5: Make a Möbius Strip by Twisting One End of the Paper 180˚ Before Taping It to the Other End. the Top Surface of the Bottom of the Paper Should Be Connected to the Bottom Surface

Step 6: Draw a Line on the Inside of the Loop. the Line Will Go to the Outside of the Loop and Back to the Original Starting Point.

Step 7: Cut Along This Line. a Single Möbius Loop With 3 Twists Will Be Created.

Step 8: Make Another Möbius Loop and Cut Along the Middle About 1/3rd of the Way Towards the Edge. This Will Create 2 Linked Loops.