Webster’s Dictionary defines tessellations as, “a covering of an infinite geometric plane without gaps or overlaps by congruent plane figures of one type or a few types.” This means that tessellations are formed when shapes are repeated to cover a flat space without overlapping each other or leaving gaps. It’s also commonly known as tiling.Historically, this style was used to create mosaics found on floors and walls.
So, are tessellations art or math?
Tessellations are all about geometry.
Although tessellations have been around for centuries, Sir Roger Penrose, a British mathematician, is well-known for his work with them. In 1974, he created aperiodic tilings, a group of tiles, whose pattern would go on forever but never repeat. This was revolutionary because, before his discovery, tessellations contained periodic tiling or repeating patterns.
Even more impressive was the fact that this was achieved with just two shapes, both created from a pentagon’s lines and angles. His most popular tile came from what he called, “kites” and “darts,” simple symmetrical geometric shapes that when tessellated according to his placing rule, worked to create beautiful designs that never repeated.
When you create a tessellation, you’re often creating a beautiful piece of art, like the mosaic.
Dutch graphic artist, M.C. Escher, is widely regarded as the most famous tessellation artist. He was passionate about filling his page with objects that did not overlap or leave spaces. His recognizable patterns are periodic tilings – they only fit together one way. Before his death in 1972, he had created 448 lithographs, woodcuts and wood engravings, and over 2000 drawings and sketches.One thing that people loved about his work was that through his tiling and shading, he created optical illusions.
People loved the fact that through his tiling and shading, he often created optical illusions.
Tessellations aren’t just about art and math. We also encounter them in our daily lives.
Everyday Objects with Tessellations
- soccer balls
Create your Own Tessellation Art Piece
It’s easy to make your own periodic tiling art project. You’ll need:
- 1 index card cut down to a rectangle, measuring 2.5″ x 3″.
- clear tape
- cardstock (this will be your art piece)
- markers or colored pencils
- black thin-tipped marker
Let’s get started!
- Take your pencil and draw a line, connecting two adjacent corners on the long side of the rectangle. This line can be wavy or straight, creating whatever design you’d like, as long as it goes from one corner to the other.
- Cut along the line and with the tape, affix the piece you just cut off to the opposite long edge, lining up both straight edges.
- Repeat the process while working on the short side. Now you have the shape you will use to create your tessellation.
- Lay your shape down somewhere on the cardstock and trace it with your pencil.
- Shift it so it lines up with the first one without overlapping or leaving any space and trace it again. Keep sliding and tracing until you cover the whole sheet of cardstock.
What do your shapes look like? Use your colored pencils or markers to bring it out and make it recognizable. As you can see, my daughter thought our shape looked like a unicorn.
Voilà! You’ve created a work of art, based on geometric principles.