Uh oh, looks like our teacher has tessellated on the floor! Luckily, this isn’t a bad thing as the floor is tessellated too! Before you reach for a mop and bucket, let’s talk tessellation!
Tessellation is the use of a single shape, to cover an area, with no gaps or overlaps.
Notice how the teacher’s dress is really made up of three colored rectangle-like shapes, while the floor is completely covered in triangles, this is tessellation. Tessellation has always been an art and fashion favorite, though can sometimes be hard to detect.
Tessellation is a favorite of fashion designers because it relies on symmetry - two or more pieces of the same object being identical, balanced and proportionate – much like the human body.
There are four types of symmetry that can create tessellation, (while lending on-trend traction to your wardrobe!)
Translation – a shape that does not turn or flip, but glides.
Reflection – a shape that’s been flipped at an angle, horizontally, or vertically.
Rotation – a pattern of shapes that appear to rotate around a certain point
Glide Reflection – a pattern created using translation and reflection.
Look at Sam Kerr’s tessellation picture made entirely of rabbits. Remembering that there can be no gaps or overlaps and that the pattern must repeat, you might be wondering how this is even possible. It all begins with one simple shape. Each of Kerr’s rabbits starts as an equilateral triangle to which he makes symmetrical adjustments until they all fit together like puzzle pieces!
Tessellation also occurs in nature. The patterns of a snake’s skin and a turtle’s shell are examples of tessellation, as are fish scales and honeycombs.
Both artists and mathematicians are fascinated by tessellation as it seamlessly combines a clear set of mathematical rules with infinite creative possibilities, resulting in one visually stimulating piece.
In the grand scheme of things, it all makes sense: People are drawn to beauty; people feel most comfortable when surrounded by order - yet art is inherently chaotic. Tessellation is the best of both worlds, lending imagination to computation!
Think of tessellation as the couture of calculations.😎 Thinking about math in relation to other interests, (like fashion) is a great way to internalize the concept and raise your mathesteem!
Can you think of any other real-world examples where you’ll see tessellation?
Photographer: @jaxonphotogroup http://www.jaxonphotogroup.com