Tessellations

This presentation is based on the work of Melissa Hogg and Miranda

Hodge

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

• Tessellations are everywhere.

• How many tessellations have you seen today?

Geometry & 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, and rotated.

• These moves, alone or combined, can create interesting tessellation designs.

Translation

Rotation

Reflection

Regular Tessellations

• Uses only one type of regular polygon • Rules:

1. the tessellation must tile an infinite floor without gaps or overlapping2. the tiles must all be the same regular polygon3. each vertex must look the same.

Regular Tessellations: Examples

Semi-regular Tessellations

• Uniform tessellations that contain two or more regular polygons

• Same rules apply

Tessellation Nomenclature

• A tessellation of squares is named "4.4.4.4". Here's how: choose a vertex, and then count the number of sides each polygon has that forms the vertex.

Tessellation Nomenclature Examples

Professional Tessellation Designs

• Many artists have created master works of art based on tessellations.

• M.C. Escher (“The Father of Tessellations”) and Robert Ingalls are two of the most famous.

Sun and Moon

M.C. Escher

Fish

Robert Ingalls

M. C. Escher

M. C. Escher

Escher, again

Transformations with Tessellations

Student Examples

Student Examples

Student Examples

Student Examples

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 5 Rico Boja Grade 2