The Mathematics of Tesselations

  At some point, we teach students to create tessellations during the school year.  I know I have.  I've had students create either a concave or convex shape and use that to create the final tessellation but I have not taken time to discuss the mathematics of tessellations.  Have you?

How do you go about teaching the mathematics behind tessellations?  What things do you need to focus on?  What are the different types of tessellations?  What prior knowledge does a student need before starting?

This 29 page pdf answers many of those questions and provides some excellent information for creating a short unit on the mathematics. It begins with explaining the knowledge students should have when beginning this unit and reviews the formulas to find the interior angles of any regular polygon.

Once it gets into tessellations, it has students explore creating tessellations using one regular polygon.  Its interesting that there are only three regular polygons that tessellate but students are expected to discover this by trying the different polygons.  The author provides the mathematics to determine mathematically if a regular polygon will tessellate.

It goes on to discuss other tessellations in detail in such a way as to show the consistency of mathematics involved.  The author includes Eshers tessellations and even creating tessellations using irregular shapes.  Each type of tessellation is detailed with lots of clear examples.   This article takes the information from the previous pdf and provides a great recap of the material.

Now for the big question!  How are tessellations used in real life?  Are they?  Yes, they are.  This web page has wonderful examples of how tessellations are used in real life.  The most obvious example is in a bee hive because every cell is hexagonal shaped.  If you notice, hexagonal is one of three shapes that tessellates using one shape.  Other examples include chicken wire but if you've ever seen a fishing net, it also tessellates a regular polygon.  What about quilts, floor tiles, brick work, or certain toys, reptile skins, decorative wire works? 


Its just a short step to having students create a final product for tessellations that might be:
a.  A presentation.
b.  A pod cast.
c. A video.
That covers :
a. Tessellations.
b. Real world uses.
c. Artists who made their name using tessellations.

So many possibilities just like tessellations.