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. Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.'Why tessellation?' you may well be asking. Have questions about the image or the explanations on this page? If you are able, please consider adding to or editing this page! Teaching Materials There are currently no teaching materials for this page. For more information, check out the separate page on Hyperbolic Tilings Tessellations can also be formed on hyperbolic surfaces. In the image below, the hexagons are white and the pentagons are black. A soccer ball is covered in hexagons and pentagons, which form a semi-regular tessellation on a sphere. Shapes can be tessellated on surfaces other than the plane, such a spheres. Examples of beautiful tessallations in nature are cracking patterns in dried mud or pottery, cellular structures in Biology and and crystals in metallic ingots.Ī larger example of Penrose tiling, which can repeat infinitely without repetition or symmetry. Tessellations are observed in some works of great artists like M.C. Tessellations are a combination of math, art and fun, in this regard there are numerous applications in real life ranging from the patterns on floors to jig-saw puzzles. The image below is an example of an irregular tessellation. Many other shapes, including ones made up of complex curves can tessellate. Irregular tessellations encompass all other tessellations, including the tiling in the main image. Below are examples of semi-regular tessellations. Semi-regular tessellations, also known as Archimedean tessellations, are formed by two or more regular polygons whose arrangement at every vertex are identical. Regular Hexagons A regular hexagon is a six-sided regular polygon, and it also tessellates.
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