Question

Make a Mobius band. Let the band be 3 cm wide. Make a lengthwise cut, staying 1 cm form the right-hand edge. Describe the result.

Short answer

Take a strip of paper. Give it a half roll. Bind the ends together. The resultant is a Mobius band. As the band is a three-dimension figure having only one side and a curved boundary when it will be cut lengthwise it will become the shape of an infinite loop which is also a three-dimension figure having no sides but having two boundary curves. Its length will be twice the length of one band.

Step-by-step solution

Step 1. Make a Mobius band.

Take a strip of paper. Give it a half roll. Bind the ends together. The resultant is a Mobius Loop.

Step 2. Cut the band lengthwise.

Cutting the Mobius strip staying 1 cm from the right-hand edge gives longer strips with two full twists rather than two separate bands.

Step 3. Describe what happens.

As the band is a three-dimension figure having only one side and a curved boundary when it will be cut lengthwise it will become the shape of an infinite loop which is also a three-dimension figure having no sides but having two boundary curves. Its length will be twice the length of one band.