By Math Is Fun, September 4, 2021

“How many sides does a paper have?” I asked my son, who was watching TV.

“2”

“What if I tell you I can make a paper have ONLY one side?”

“No Way!”

“Come and I will show you how to make a Mobius Band.”

Well we are in the year 2021, so there is a Youtube video for everything. There is no need to repeat what I told my son. I can simply refer you to a video created by other people. For example this one:

“Now let’s see how many sides the band has. Draw a line like this. Notice there is only one line and it covers the entire ring. While on a normal circular ring, you need two lines to cover the two sides.”

“Now use a scissor and cut along this line. Tell me how many pieces it turns into.” I said.

Son cut the paper, and it transformed into one ring instead of two!

Bonus experiment: try cutting a Mobius band with a line that is ⅓ of the width to the side instead of the center line, see what it turns into.

There is a branch in Math called topology. Put into simple (but inaccurate) terms, Topology studies spatial properties of stretch-able objects. It’s not important what shape the object is, it can be square or round. There are properties an object displays regardless of the shape. That might be too complicated for a kid. They only need to remember Mobius band is a very famous example used in Topology. And here is another famous example:

This is called a Klein Bottle – a bottle that can never be filled up! Notice that if the water fills up, it will raise above the handle, and the handle is connected to the outside! You can buy a Klein Bottle on Amazon and experiment yourself.