Tessellations Explained

By Roseann Krane, Monte Vista High School, Danville, CA

and Jeff Ng, Mike Carns, and Amber Bullington

Tessellations are a mixture of a common shapes used to create a pattern on a plane. For example, if we take squares and layer them on the floor, we can cover the entire floor with it, without any space leftover.

We can do the same with triangles and hexagons.
A hexagon is essentially six triangles placed together. The only requirement for a tessellation is that it covers the entire plane. It can be made of many shapes...

Or one shape, modified to fit.

Again the only requirement of creating a tessellation is that the pattern covers the entire plane, with no spaces or overlapping anywhere.

Translational transformation

Translational means a movement in position. That is, a movement on the plane. So, if we start with the squares...

And then we cut one slice out, and put it on the other side...

Then it will still be a tessellation, covering the entire plane without overlap or extra spaces.

This is called "Translational Transformation"

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