The Marvellous, Mathematical, Mobius Strip!

Mobius strips are fun little objects with some very surprising properties. Best of all, they are super easy to make… all you need is some paper, a pair of scissors and a glue stick. Read on to get started!

Making Your Mobius Strip:

  1. Start by cutting your paper into long strips, 2-3cm wide. The longer you can make the strip, the easier it will be to put together
  1. Mark an “X” at each end of the strip. Connect the ends of the strip together, twisting the paper so that the “X” s touch each other
  1. Secure the ends with glue. Congratulations, you’ve just made a mobius strip!

Now that you’ve made your mobius strip, it’s time to have some fun.  

How many sides?

Draw an “X” anywhere along the centre of your mobius strip. From this mark, draw a line along the middle of the strip. Try not to remove the pen from the surface of your strip as you do this.

Eventually you will arrive back at the “X” you started at. What’s more, even though you didn’t flip the paper over, you will see that the line is on both sides of the mobius strip. What’s going on?!!!

Remember how we said that your mobius strip has some surprising properties? Well, one of those properties is that even though it looks like it has two sides, thanks to the twist you added when making the strip it actually only has one. It also only has a single edge. Don’t believe us? Test it yourself by tracing the edge of your strip with your finger or a pen. Neat huh?

But wait, there’s more!

Grab a pair of scissors and carefully cut along the centre line you just drew. Don’t stop until you reach the point where you started cutting again. What happens?

Now, you might have been expecting to end up with two, separate (albeit thinner) mobius strips. Instead, what you actually get is a single loop that is twice as long as your original mobius strip.

Weird right? Well, it gets weirder…

Whoa, what the?

Make another mobius strip and grab your scissors again. We are going to cut our strip again; except this time you are going to start cutting about a third of the way in rather than straight down the middle.

Keep cutting the strip in a spiral pattern until you reach the starting point of your cut. What has happened this time?

Just like last time, our strip has turned into a long loop. Unlike last time, this time, we also still have a short mobius strip wrapped up in it!

What’s going on?

By adding the twist to your mobius strip when you made it, you effectively joined the two sides of the piece of paper to each other, making one side that was twice as long as the original strip, and with only a single edge. By cutting it down the middle, you added another edge back to the strip giving it two sides again but keeping the effective length of the mobius strip.

Confused? That’s ok. Although the construction of a mobius strip is simple, the mathematics that describe them are surprisingly complex. So complex in fact, that the humble mobius strip even helped to inspire an entire field of mathematics called TOPOLOGY!

So there you go! You now have everything you need to wow your friends and family with your own Marvellous, Mathematical, Mobius Strip. If you do create your own Mobius Strip we’d love to see it. Make sure you snap a pic or even record a video of your experiments and upload it to your social using #motatfun (don’t forget to ask your parent’s permission first though.) so we can check it out!