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.
