A Möbius Trisection

Strategies and Hints

  1. Trisecting a Möbius strip results in two strips. The smaller has one half twist and is identical to the original strip. The larger strip is twice as long and has 4 half twists.

  2. Bisecting the smaller band would give just one band. The larger band (with the 4 half twists) will become two bands when bisected.

  3. Yes.

Solution

No. One of the two resulting pieces is equivalent to the original band. The other is a different structure.

 

McGraw-Hill/Glencoe The McGraw-Hill Companies