Where’s the Math??
Presentation by Melissa Hogg, Curr 383 E
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?
• 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?
Math in Tessellations
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
Translation • Symmetry is an important part of tessellations. • Geometric shapes can be translated, Reflection reflected, rotated, or glide reflected. • These movements of the shapes creates a more interesting tessellation design. Glide Reflection
Rotation
Professional Tessellation Designs
Sun and Moon
M.C. Escher
Fish
Robert Ingalls
• 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?
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
Curriculum Links
Tessellations can be used in either elementary school or high school. Teachers would have to either simplify or expand the lesson depending on the age group.
Arts Subject Area • Visual Arts
Math Subject Area • Geometry and spatial sense • Patterning and Algebra
References
Michael Saiki Grade 5
Lizards M.C. Escher
Rico Boja Grade 2
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.html
Modern Day Artists Inspired my MC Escher
www.geocities.com/davidschow/HUB/Esample.htm