Just as I think of Scott Kim when I think of symmetries, I cannot help thinking of Maurits Cornelius Escher when I think of tessellations. His artistic tessellations make the concept ‘come to life.’ I like the way that he plays with shapes and meaning … and I hope you do, too!
This image is called Clowns, but he produced many tessellations and other mathematical images as well. Please visit the official M C Escher website which has been set up to preserve and display his work. There you will be able to learn about the man and view many of his wonderful artistic creations. Please note that all Escher’s works are still copyright and the copyright is owned by The M.C. Escher Company, B.V. which operates the official website. They have kindly granted me permission to use this image.
A shape that is tessellated is one that can cover a plane in an interlocking way with no gaps. Sometimes there are two shapes, or three that tessellate together, and Escher explored all these possibilities.
You will notice that Clowns has been based on equilateral triangles (since Escher did not erase his construction lines). Equilateral triangles tessellate, of course, since they can easily cover a plane with no gaps. There are other shapes … squares for example … that tessellate, but can you think of others? Try joining squares together into units. For example, three squares can form a V shape which tessellates. What about four squares producing an L shape? Does that tessellate? You might experiment with equilateral triangles as well.
Once you have a basic tessellating shape, you can begin to distort it in different ways and that is where the creativity comes into play as well. I will be adding material here to give you ideas about how to explore the mathematics of tessellations … and how to create some of your own!
Our son Joshua is currently in year 11 preparing for the HSC. Josh was doing reasonably well in mathematics and yet we felt, and his teachers agreed, that if he really applied himself he could be achieving much better results. We asked around for a maths tutor and Graeme Henderson came highly recommended. Joshua began to see Mr Henderson one hour per week and from the very first week Joshua’s motivation escalated. His maths improved to the point where he is now often achieving 100% in his exams, he applies himself to do hours of homework, something he had rarely done in the past, but most of all Josh has found a love of mathematics. Maths is no longer a chore. I believe this all stems from Mr Henderson’s gifted ability not only as a teacher, also as an encourager and motivator. I get motivated just listening to them! Josh told us this week that he wishes he could be tutored every day after school. When the results come through from Joshua’s exams, he is delighted and this has inspired him to become motivated to spend much more time applying himself to his other subjects. Josh is working hard to gain a great result in his HSC. I can personally recommend Mr Henderson as a truly wonderful tutor.
Deborah B (Parent, 2012)
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