# Merry Möbius Strip Ornaments and Garland

We love a project that looks cool, has a WOW moment, requires no special materials or complex instructions, and educates. In this case, our project is also a celebration of the holidays. So it is a win on all fronts! Today we are making Möbius Strip inspired Christmas decorations including garland and ornaments. No matter what holidays you are celebrating, these festive, magical math inspired decorations are going to be a hit!

## DIY Möbius Strip Christmas Decorations

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The holidays are coming and everyone is so busy. If you are looking for a project that is simple, requires no prep or special materials, and includes some fascinating lessons in mathematics, we found the answers in the Möbius strip!

It’s one of those seemingly simple objects that is actually a real mind-bender. It is so simple that you can create one with just a strip of paper and a bit of tape. At first glance, it seems like any other loop, but it hides an incredible secret… it has only one side and one edge! Crazy, right? Trust me, this is a big wow moment for kids!

## Understanding the Möbius Strip

Do this exercise with your kids. Have them hold a strip of paper, you can clearly tell which side is the front and which is the back. It has two sides (I can just imagine your students rolling their eyes right now).

Take that strip of paper and tape the two ends together. You now have a circle of paper and you can easily tell which is the inside surface of the circle and which is the outside surface of the circle (those eye rolls are epic by now I am sure!).

But take the same strip of paper and before you tape it into a circle, do one flip of the paper on one side, then tape it into the circle. Now we have a Möbius strip, and the two sides magically become one side and one edge!

Take a pencil and try drawing a line through the middle of the Möbius strip. You never have to lift your pencil as you draw a line through all of the surfaces. A Möbius strip is a loop-de-loop of mathematical wonder, like a never ending rollercoaster!

Want an even bigger wow moment, try cutting along that line so you are cutting the Möbius strip in half. Have your students predict what they think will happen. It should become two pieces right? Wrong! It is still one piece. No eye rolls now are there?

Now we are going to use this amazing Möbius strip to make Möbius Garland and Möbius Strip Ornaments for the holidays.

## Tutorial Video

Check out our tutorial video for this project. If you can’t see the video your firewall or adblockers are blocking the feed. You can also find this video on the STEAM Powered Family YouTube Channel.

## Möbius Strip Decoration Supplies

All you need for this project is:

Strips of construction paper in festive colours. We made our strips about an inch wide.
Tape
Glue stick (optional)
Pipe cleaners or string (optional for hanging the ornaments)
Markers (optional)

## Making Möbius Garland

In this activity we decided to take two colours of construction paper and glued them together. Then we made the links as Möbius strips. Simply make the first Möbius strip, then loop the paper of the next link through the first, give it a twist and tape it. Continue as you make your garland.

Another alternative is to have your students write messages on their strips before turning them into a Möbius strip. These could be wishing for the holidays, popular phrases or even their names. Then link them together into infinite loop Möbius garland to decorate your classroom. When writing your messages, write it on one side, then flip it away from you, so when you start writing on the reverse side, your words start on the same end but are upside-down. See the video if this is confusing.

## Making Möbius Strip Ornaments

A fun project your kids can do as a take home project is to make a Möbius Strip Ornament.

All you need to do is make a take a strip of construction paper in festive colours (you can glue to coloured strips together if you wish), then do a single twist as you form it into a loop then tape the two ends together. You can also write festive messages on your strips of paper before you shape them. Just make sure you flip it the way we explain in the garland section or see the video for a demonstration.

Want to do even more? Learn how you can make Möbius strip hearts!

## Möbius Strip Math Explained

Now, let’s dive a bit into the math that makes this object so intriguing. The Möbius strip is a prime example of a non-orientable surface. In mathematics, “non-orientable” means that you can’t distinguish between the two sides of the surface, because, there’s only one surface.

Topology, is the branch of math dealing with properties of space and shapes. The Möbius strip is different from a simple loop or circle of paper, which has an orientable surface (you can tell which is outside and which is inside). In topology, you could stretch and deform the shapes all you want, and they’d still fundamentally be the same. It’s like how a circle can be stretched into an ellipse; they’re still fundamentally equivalent in a topological sense.

It’s also super interesting how this one-sided wonder finds its way into various applications. In conveyor belts, for instance, a Möbius design can ensure even wear and tear. Even in the realm of art and literature, the Möbius strip has served as a metaphor for infinity and the interconnectedness of all things.

I found this incredible video from Ithaca College of a massive Möbius strip. It is mesmerizing!

Have fun bringing a little extra magic to the holidays this year with math and the Möbius strip!

Want more festive math? Try Geome-Tree a 3D Nets Ornament making project.

Happy Holidays!