# Regular Tessellation Write-up

From EscherMath

Jump to navigationJump to searchIn the exploration Angles of Polygons and Regular Tessellations Exploration we see that there are only three regular tessellations. The exploration is really an outline for a proof.

After doing the exploration, your assignment is to provide the justifications and details of the arguments. Below are 5 steps that make up the general argument. Write down a short paragraph for each step showing why this is true.

- Step 1 – In every n-gon there are n-2 triangles (this is the best case scenario)
- Step 2 – The sum of the angles in an n-gon is (n-2)*180
- Step 3 – If our n-gon is regular, then the angle measure is exactly (n-2)*180 / n
- Step 4 – Show that the angles associated with the 3-, 4- and 6-gon are the only ones that divide 360.
- Step 5 – Show that this means that only 3-, 4- and 6 gons give regular tessellations