Question

Give a full twist to a long, narrow strip of paper. Tape the ends together. How many sides does this band have? Cut this band lengthwise down the middle. Write a brief description of what is formed.

Short answer

Band has only one side. Cutting the band down the middle gives a longer strips with two full twists which forms a loop.

Step-by-step solution

Step 1. Number of sides of band.

If you join the ends of a twisted long narrow strip of paper, you get a three-dimension figure which has one side and having one boundary curve.

Step 2. Cut the band lengthwise down the middle.

Cutting the band down the middle gives a longer strips with two full twists rather than two separate bands.

Step 3. Describe what happens.

If you join the ends of a twisted long narrow strip of paper, you get a three-dimension figure which has one side and having one boundary curve which on cutting becomes a loop.