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What procedures can you use to create your own tessellations?

To create your our own tessellations, you could use regular polygons, but that would get boring rather fast. It's much more fun to get creative with your shapes and patterns and make a design that defies regular polygons. All you have to do is follow the steps in this video.

As you watch this video, use the study guide to follow along if you'd like. Click the button below to download the study guide.

PDF Download In this video, I will share with you a method to create a symmetric design that can tessellate a plane. To start, you will need a square piece of paper with letters that label each corner. I chose to use the letters R, A, T and S so that it spells "rats" – and you will see why in just a moment. Next, you will need to draw a line from the top of the square to the bottom and from the left of the square to the right. It can be curved, or jagged, or even a straight line drawn on a diagonal… We will cut along these lines next to separate the square into four pieces. Keep this in mind when deciding how intricate to draw your lines. This is what my design looked like when I cut it apart… Next we need to rearrange these four pieces by moving them diagonally from where they began… Since my pieces spelled "rats" at the beginning of this project, they now spell "star" when rearranged. Tape these shapes back together in their new orientation. This newly formed shape will now tessellate a plane by translating horizontally, and vertically. Trace the shape you completed in the upper left hand corner of a sheet of paper and then slide it to the right, or down to trace again… Repeat this step as many times as needed. Using two highlighters and a pencil, I added color to my tessellation. Now go ahead and add some art to yours. Perhaps you might try a striping or crosshatch pattern to add an artistic touch to the design. Good Luck!

Transcript

Question

How many times do you need to repeat the pattern to finish your tessellation?

Enough times to cover the entire sheet of paper.