TESSELLATIONS

Background
Art and mathematics can be combined in designs that are a fascinating mix of detail and beauty by creating tessellations.

To make a tessellation you need to create a pattern of repeating shapes which leaves no spaces or overlaps between its pieces. Tessellations are made by reflecting (flipping), translating (sliding) and rotating (turning) the two-dimensional shape or shapes that you choose to use. Your choice of colours for each of the shapes adds further beauty to your design.

Here are some examples of tessellations.
Look at each of one carefully and discuss with a partner the shapes that you can see.

Using regular polygons and circles	Using polyominoes	Being inspired by the work of artist MC Escher	Using a design you can create yourself based on a square
Composition of Grey and Light Brown   1. Copyrighted image reprinted with permission citation	English Tilings, Holy Trinity, Leeds 2. Copyrighted image reprinted with permission citation	Twisted Squares 3. Copyrighted image reprinted with permission citation	Koch Snowflake 4. Copyrighted image reprinted with permission citation
Designs in Tile - Commercial Bath Installations   5. Copyrighted image reprinted with permission citation	Chinese Pattern 6. Copyrighted image reprinted with permission citation	Fish by MC Escher 7. Copyrighted image reprinted with permission citation	Optical illusion  8. Copyrighted image reprinted with permission citation

Tessellations in History

Geometric and artistic shapes and patterns, including tessellations, have been used by people for thousands of years to create beautiful tiles. Visit the following website and look at the range of tiles created by people from many lands and during different times in history.

Discuss with your partner the shapes and colours that have been used in each set of tiles.
Discuss which ones you like best and why?
Find other examples of tessellations within your school, home and community environment.

A town in your area has experienced a flood which has destroyed the carpet in the children's book section of the town library. The local council has decided that it will replace the floor covering by using tiles instead of carpet. The council has announced a competition which will involve people in designing a new tile pattern that could be used to cover the floor in this section of the library. You have decided to enter this competition as the council is offering a prize of $2 000 for the winning design.

Before creating your design you will need to investigate the following to help you:

• how to make tessellations using regular polygons by themselves
• how to make tessellations using circles and more than one regular polygon
• how to make tessellations using polyominoes (dominoes, trominoes, tetrominoes, pentominoes etc)
• how to make tessellations using the work of the artist MC Escher
• how to make tessellations by creating your own design beginning with a square
• practice making a range of designs from which you can choose your best one

Your Presentation

You can make your design using a range of materials

• draw the design, by hand or computer, on plain or grid paper and colour it OR
• create your design using pieces of coloured paper or cardboard; wooden blocks etc OR
• use one of the following software programs to create your design (these links will take you to a tutorial that will teach you how to make tesselations using these programs). Claris Works and Tessellations or HyperStudio and Tessellations OR
• create your own method of presenting your design

When you have completed your design, write a brief explanation including the following:

• why you chose the design you have made
• why you chose the colours you have used
• why you think it will be the best design for the children's book section of the council library

Outcomes - Mathematics Years K-6 Stage 2 - Space and Geometry Two Dimensional Space SGS2.2a - Manipulates, compares, sketches and names two-dimensional shapes and describes their features Students learn about: constructing two-dimensional shapes from a variety of materials eg plastic, cardboard making representations of two-dimensional shapes in different orientations using a variety of materials and drawings making tessellating designs by reflecting (flipping), translating (sliding) and rotating (turning) a two-dimensional shape Students learn to: recognise that a particular shape can be represented in different sizes and orientations (Reflecting) manipulate two-dimensional shapes using the cut, copy, paste and rotate functions in a computer drawing package (Applying Strategies) describe designs in terms of rotating, reflecting and translating (Communicating)

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