1512 Geometry and Tessellations

I've always enjoyed doing geometry and I'm amazed by how geometry surrounds us everywhere. I really enjoy the process of figuring out an answer rather than just plugging in numbers into something. One thing that has sparked my interest, that I wasn't really aware of before, are tessellations. I've never really put much thought into them, but I think they are really neat on how they work out.

Think of the last puzzle you put together, that is a tessellation. A tessellation is when you put together geometric shapes, so that when you are finished there are no gaps in between each shape. Now, that is a very basic definition and not too mathematical so, we must have some rules for a regular mathematical tessellations to exist.
1. Tessellations must be a geometric figure that fits together without gaps or overlaps and covers an infinite plane.

2. The geometric figures must be regular polygons and the same.

3. The vertex must look the same.

Equilateral triangles, squares, and hexagons are all great examples of regular tessellations, but you can combine different regular tessellation shapes to make a semi-regular tessellation.

Wait a second, I've seen this before. This looks like when you tile a floor or a shower. Who knew this was a tessellation? Now that I'm aware of them, I started noticing them more and more in everyday life, like on this McDonald's commercial. Again, geometry surrounds us in so many ways. I found a great educational website that allows students to create their own semi-tessellations.