Where’s the Math??

What Is a Tessellation?

• A shape or tile that repeats to fill a surface without any gaps or overlaps.

• The name comes from the word tessella, the small square tile used in ancient Roman mosaics.

                               

Tessellations Around Us• We are exposed

to tessellations everywhere.

• Do you recognize these common tessellations?

• How many tessellations have you seen today?

Math in Tessellations• Many different geometric shapes can be

used to create tessellations.

• Which of the shapes below would fit with itself to make a good tessellation design?

Patterns

• Very basic tessellations are simply a repeating pattern.

• The rule is that you have to make sure that the shapes fit together leaving no open space on the page.

Symmetry• Symmetry is an

important part of tessellations.

• Geometric shapes can be translated, reflected, rotated, or glide reflected.

• These movements of the shapes creates a more interesting tessellation design.

Translation

Rotation

Reflection

Glide Reflection

Professional Tessellation Designs

• Many artists have created master works of art using the simple rules of tessellations.

• M.C. Escher and Robert Ingalls are among many tessellation artists.

• Can you you spot the repeating shape?

Sun and Moon

M.C. Escher

Fish

Robert Ingalls

You Can Be a Tessellation Artist

You need to first create a tessellating template.• Step 1: using grid paper cut out a perfect square. • Step 2: with a pencil make a line on two adjacent

sides of the square. Be sure not to draw through a corner.

• Step 3: cut out the pieces and attach them with tape to the opposite sides from where they came.

You have now created your tessellation template.

Seeing a Figure• Looking at your tessellation template, study

the sides and the shape to decide what sort of figure you might see.

• The person who designed this form saw an elephant and an elf.

• Are there any other different forms that you might see?

• When looking for the shape be sure not to see too much detail as it can make the art work too crowded.

Putting It All Together• Take your

tessellation template and trace it on to a piece of paper.

• When tracing you can use different types of symmetry to change your picture.

• Be sure that your whole page is filled with a repeating pattern.

• Colour in your picture creatively.

Elephants

Translation symmetry

Elves and Elephants

Combinations of symmetry

References

Beyer, Jinny. Designing Tessellations. Chicago: Contemporary Books, 1999.

Britton, Jill. Escher in the Classroom. http://ccins.camosun.bs.ca/~jbritton/jbescher.htm

Math Forum mathforum.org/sum95/suzanne/tess.intro.htmlModern Day Artists Inspired my MC Escher

www.geocities.com/davidschow/HUB/Esample.htm

Michael Saiki

Grade 5Lizards

M.C. Escher

Rico Boja

Grade 2