A tessellation is a repeating patterns of shapes covering
a plane without any gaps or overlaps.
Normally, tessellations are created using polygons
(see example on left). However, the tessellations on Alphabet Geometry
are created with letters. What you will see below is a lesson on how
to create a tessellation using the letter N and a series of transformations.
It does not teach about the different types of tessellations or about
what shapes will tessellate; it simply shows how to use transformations
to create a your own tessellation.
What is a transformation?
If you haven't already checked the transformations
section of this site and learned about reflections, rotations, and translations,
please do so now. Without previous knowldege of transformations, what
follows will make no sense.
Below is the tessellation that we will create in this
lesson. Notice that it has a repeating pattern and no gaps or overlaps.
The entire tessellation was created using transformations. Let's find
out how.
Step One: Transforming
Shapes
Many transformations are created when a simple shape is modified on
one side and then the modification is either translated,
rotated, or reflected to another side. See the example below.
By using a translation,
we can make this square turn into the tessellation to the right.
Use the buttons below to see the how to turn
the square into the shapes on the right.
Step
Two: Using Transformations to Create Letters
We can also use transformations to create letters. Starting with a basic
shape, we can then apply one or more transformations to the sides of
the shape to create a letter. In this case, we'll create the N in our
tessellation.
Step
Three: Using Transformations to Create the Tessellation
You've seen how transformations can create the letter N. Now let's see
how to create the entire tessellation using a series of transformations.
In order, they are a reflection, two translations, a rotation, and two
more translations. Click play to watch.
