This is one of the simplest types of tessellation. The rectangles are translated diagonally to produce the entire image. This tessellation consists of interlocking rectangles which contain the fish and boat images. Subsequently, his pictures contained more shapes, which were often transformed by reflections, rotations and translations. In 1936, Escher made a second trip to Alhambra. Rather than drawing what he saw, Escher started to express ideas he had in his mind, creating spatial illusions and detailed repeating patterns. Gradually, Escher's work began to change. However, on a visit to Alhambra in Spain, he became fascinated by the Arabic tessellating patterns contained in the tiles, and started to experiment more with shapes and mirror images. Born in 1898, initially he concentrated on sketching scenery and surrounding objects. This in itself makes a lovely investigation for children.Īnother remarkable man who contributed enormously to the study of tessellation was the Dutch artist M.C.Escher. The two shapes are both parallelograms and the tessellation is often referred to as "Kites and Darts" :Īlthough there are small repeated sections, there is no single unit which can be copied to fill the plane. Amazingly, he managed to reduce this to only six, then just two. Using only pencil and paper, Penrose found such an arrangement but it contained many different shapes. This kind of tessellation became known as quasi-periodic, in other words at first glance there appears to be a repeating pattern, but in fact He began by investigating combinations of shapes which would produce a repeating unit, but this led on to a search for a pattern with no repetition. While studying for his PhD at Cambridge, Penrose became fascinated by the geometry of covering a plane. Octagons and squares can be arranged to form a semi-regular pattern: The image that we are likely to think of is known as a regular tessellation, where all the shapes are regular and of the same type, for example:Ī semi-regular tessellation is made up of two different regular shapes and each vertex (i.e.
Traditionally, the pattern formed by a tessellation is repetitive.
Two people have principally been responsible for investigating and developing tessellations: Roger Penrose, an eminent mathematician, and the artist, M.C.Escher. Tessellations are a common feature of decorative art and occur in the Presumably this is an indication of the fact that tiles of this shape are the easiest to interlock. The word tessellation itself derives from the Greek tessera, which is associated with four, square and tile. Tessellation is a system of shapes which are fitted together to cover a plane, without any gaps or overlapping. And of course, there is so much maths involved! It seems a golden opportunity to link art with maths, allowing the creative side of your children to take over. There is so much scope for practical exploration of tessellations both
For many, this is their preferred method of learning and, in general, it engages pupils more effectively. So often in the classroom we try to make activities more enjoyable for the children by varying our teaching to include a more tactile or "hands on" approach. 'Why tessellation?' you may well be asking.
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