## Tessellation explorer

By David Shaw, 28 August 2015

Make a sum that adds to 2.

Think your bathroom is boring? Try tons of terrific tessellations and show that tiling is styling! Find out more about the maths of tessellation in this hands-on maths activity.

### You will need

### What to do

Trace the shapes you selected.

- Look at the shape sheet. There are several fractions on the picture – 1/3, 2/4, 3/5 and so on. Do you notice a pattern in these numbers?
- Add some of the fractions together to make 2. You can add the same fractions several times if you need to. This might be easier if you use the smaller fractions rather than the larger ones.
- Once you’ve checked your sum, find the shapes that correspond to them. For example, the sum 1/3 +2/4 + 2/4 + 4/6 = 2 corresponds to one triangle, two squares and a hexagon.
- Trace these shapes onto tracing paper, and cut them out. Arrange the shapes so they all touch at one corner without overlapping.
Put your shapes together so they meet at one corner.

- Trace and cut out more copies of the same shapes. See if you can extend your shape pattern in all directions without gaps or overlapping.

### What’s happening?

When shapes fit together without gaps or overlapping, we call it a tessellation. There are three regular shapes that tessellate with themselves – triangles, squares and hexagons. To get other regular shapes to tessellate, you need to use more than one shape at a time.

Cut out more shapes and extend the pattern.

There are lots of different ways to tessellate with two or more shapes. Mathematicians give these patterns different names such as semi-regular tessellation, and demi-regular tessellation.

The fractions in this activity are related to the angles on each shape. If you multiply each fraction by 180, you get the angle in degrees. For example, the square has the fraction 2/4 written on it. 2/4 x 180 = 90 degrees, the size of the angles in a square.

When you find a set of fractions that add up to 2, you will be able to arrange the corresponding shapes to meet all at one point. The angles meeting at that point will add up to 360 degrees.

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