After we read about tessellations in The Great Number Rumble: A Story of Math in Surprising Places we decided to make our own artistic versions. I got the directions from Big Ideas for Small Mathematicians.
Tessellation is about regular patterns that split the plane up into lots of little tiles which fit together perfectly, without overlapping or leaving any gaps. Tessellation is fundamental to maths, because it’s all about symmetry.
We started with a cardboard square each (ours were about 5x5cm). We talked about how we could cover a page with squares without leaving any gaps.
First we cut a piece from the bottom of our square. We were careful not to cut the corners off, and we found it easiest to cut from corner to corner (to avoid having to measure where to reattach the cut piece on the other side). We slid the cut-off piece upwards, and attached it with tape to the top edge of the square.
Then we did the same on the left side of our square. We cut a piece out, slid it along to the right side, then reattached it.
I asked the children if we had added any cardboard to our shapes, or taken any away (no). We agreed, then, that our shapes should take up the same total amount of space as our original squares.
We traced around our shape on a blank piece of paper, then carefully moved it along and traced around it again. And again, and again until we’d covered the page.
Our tessellations looked so pretty, we decided to paint them.
J(8)’s didn’t cover his paper without gaps – he was adamant he wanted to create his art his way – but he understood the idea!
The artist M.C.Escher used tessellation to create amazing art. This BBC video clip is excellent!
Mathematicians know that their subject is beautiful. Escher shows us that it’s beautiful.
Prof. Ian Stewart, University of Warwick
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