The Transformation Geometry project is an integral part of the Yr10 Mathematics programme at Tamaki College. It allows the students to apply their skills and knowledge of Reflection, Rotation, Translation and Enlargement, learnt formally in class, to a practical situation, in this case of creating a design on a square tile. With further applications of Rotation and Translation, identical tiles are tessellated to generate more intricate patterns.
Transformation Geometry and in particular the symmetries that are produced, underlies the arts and crafts of all cultures. It influences paintings, sculpture, music, dance and poetry and is an important tool of geologists, archaeologists, physicists and of course mathematicians. In a more everyday situation, Transformation Geometry is used to produce fabric, wallpaper and wrapping paper designs.
The construction of these patterns is simplicity in itself, no “artistic bent” is needed, just some Mathematics. First a simple motif is formed, literally any “squiggle” will do. A template of the motif is made out of cardboard. This is placed on a square in any chosen position and using guidelines and points, the template is reflected, rotated or translated or a combination of these. During this process, the motif often overlaps itself creating a variety of regions. Using colour creatively further defines the design. One individual tile, though may be very attractive in itself, is only an element in the overall pattern created by the tessellation and one individual tile can generate an almost endless number of different patterns. The students created the original patterns by hand, technology has perfected them.
Over the years a great variety of exceptional patterns have been designed by the students, which regrettably have disappeared into oblivion. When compared with commercial publications, the students designs often surpass these both in design and structure and visual effect. Therefore it seems a good time to publish some of the students work, hence the creation of this calendar.
All of the designs made by the students at Tamaki College, in 10KKo were used for publication is this calendar.
We hope that this Calendar will give you pleasure throughout the year and remind you of how Mathematics can be used to tap the hidden talents of our students.
These calendars were created in Mrs. David's Maths class using Adobe Illustrator.
We are selling the calendars in school for $10.00
Here is a preview of what the finished calendar looks like.
This is a great extension of a very neat project. It was a stroke of genius to create something that is not only useful, but that shares your students work! Kudos!
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