Tessellations

Tessellations

Create your own tessellation inspired by M.C. Escher’s mathematical art!  


What's going on?


A tessellation is a pattern made up of geometric shapes that completely, and perfectly, tile an area (no gaps, no overlaps). Your home-made tessellation has a "periodic tiling," because its pattern is repetitive, though other tessellations can be much less repetitive. Tessellations can be found in art dating back to Ancient Rome, and many popular examples of tessellations were crafted by the Dutch artist, M.C. Escher.


While it's fairly easy to make your own attractive tessellations, these patterns can also be used to illustrate a wide variety of mathematical concepts, from relationships between shapes to the rules that dictate different types of symmetry. Interestingly, M.C. Escher didn't think of himself as a mathematician, even though he had numerous mathematician friends. He even carried out research on some of his own tessellations — proof that art can provide a window into the world of mathematics for people who might otherwise avoid numbers and theorems.

Ages:
5 - 8
Est. Time:
<1 hour

How we did it:

Materials List

  1. sticky notes
  2. pencil
  3. scissors
  4. paper - large
  5. marker
  6. crayons
  1. To make a one-sided tessellation, start at one corner of the sticky note and draw a line to an adjacent corner. The line can be curvaceous, geometric, or both. 

  2. Cut on the line. 

  3. Take the piece you just cut and move it to the opposite side of the sticky note. Then, tape it to the rest of the sticky note. This will be the template for your tessellation. 

  4. Using your template and a marker, trace it in the center of a large piece of paper.

  5. Continue tracing the template so that the shapes on your paper fit together. This is a tessellation! 

  6. When you have filled your paper with tessellated shapes, color them in! 


    Optional: For more of a challenge, try fitting an animal inside your tessellating shape.

  7. To make a rotating tessellation, start at one corner of the sticky note and draw a line to an adjacent corner. From that corner, draw a second line to its adjacent corner.


  8. Cut on the lines. 

  9. Take one of the pieces you just cut and rotate it towards the adjacent uncut side of the sticky note. Then, tape it to the rest of the sticky note.

  10. Take the other piece you cut and rotate it towards its adjacent uncut side of the sticky note. Then, tape it to the rest of the sticky note. This will be the template for your tessellation. 

  11. Follow steps 4-6.