Möbius Shorts

Here is a fantastic little model similar to a Möbius strip. It is worth trying this one yourself. See if you can guess what will happen when you cut this.

Steps

1. Cut a large "T" from a piece of paper with the upright and the crossbar each about an inch (2.5 cm) wide.
   
2. Tape the crossbar's ends together in an untwisted loop.
   
3. Snake the vertical part of the T through the hole (again no twist) and attach it to the opposite side and opposite edge of the loop.
   
4. Cut the pieces along the midline of the bands as you would cut a Möbius strip.
   

Notes

• This model is topologically equivalent to a Klein bottle with a hole in it.
  

References

• (Pickover 2006, 95-6), (Boas 1995)