Allow the kids to experiment with using different shapes and tessellating them differently to create tessellations. Space out the shapes on the page and your tessellation pattern is ready. Paint the shape using the fill color option. Select the custom tools option from the tool bar, select a shape that you would like to use for tessellations, drag and drop the figure, and create multiple copies of the same. The other way is to use the MS Publisher tool. The easy way out is to find an image, copy it onto your machine, and take multiple printouts of the image to use in the tessellating activity. One way is to browse the Internet and search for online images of tessellations. You could also use your computer for tessellation activities. Encourage the kids to experiment with different shapes and perform similar calculations to find whether a particular type of polygon can be used for regular tessellations or not. Conclusion – squares can tessellate a surface uniformly while pentagons cannot. The interior angle is 108° and number of sides meeting at the vertex is 3. On the other hand, for an irregularly tessellated figure, it won’t be so.įor example, in case of a square, the interior angle is 90° and the number of sides meeting at each vertex is 4. For a regular tessellation, the product xy will be 360. Then ask them to measure the interior angle of the polygon used for tiling, say y. Also, after the surface is tessellated, ask the kids to count the number of sides that meet at each vertex in the tessellation, say x. Well, regular shapes like triangles, squares, and hexagons tessellate naturally while irregular shapes have to fit into each other to tile a surface uniformly. With this tessellation art, you’ll be bringing together tessellations and math, as the kids will understand the difference between tiling with regular and irregular shapes. But here, you’ll have to ensure that the shapes complement each other, i.e. Or ask the kids to cut irregular shapes for the tessellations. Cut one for them and then ask the kids to cut multiples. You could vary the activity by cutting out shapes of animals and birds. Would you consider it to be the gaps left by the tiled pattern, making this tessellation an semi-regular one? Or would you think of this as a pattern of cross or plus signs fitting into one another, making this a regular tessellation? Observe the white space around each shape. It also led to studies in types of tessellations (regular and semi-regular) and which shapes can be used to make tessellations and how. His work led to further study of tessellations from the mathematical point of view. Federov, a Russian crystallographer proved that tessellation of a plain can be done in any of the 17 groups of isometries. They are closely associated with math and crystallography as well. Tessellations are not limited to just art. Nikolas Schiller is an American map artist known for his kaleidoscopic aerial photography, which can be called an indirect application of tessellations. Examples of tessellations are found in ancient and modern art.Īrtworks of the Dutch graphic artist M.C. Tessellations in the form of tiled walls and flooring are part of ancient architectural styles and designs. The word ‘tessellation’ is derived from the Latin word tessella, which means a small cubical piece of clay, glass, or stone. Each surface of the cube is a regular tessellation of squares. The interior angle of the equilateral triangles and the interior angle of a square `90+90+60+60+60=360` so this pattern tessellates.A Rubik’s cube is an interesting example of tessellations. Here is a tessellating pattern made from equilateral triangles and squares.Įxplain why equilateral triangles and squares can form a pattern that tessellates.įor a group of shapes to tessellate the interior angles of the shapes around the common vertex must add up to this example the common vertex is at the centre of 2 red equilateral triangles, 2 yellow squares and one blue equilateral triangle. As the interior angles of an equilateral is a whole number so equilateral triangles will tessellate. Here is a tessellating pattern made from equilateral triangles.Ī) Write down the size of each interior angle in the equilateral triangle.ī) Explain why equilateral triangles tessellate.Ī) Interior angles of a an equilateral triangle has equal length sides all interior angles are equal, so each interior The interior angle of a shape which meets the common vertex must divide into 360 to produce a whole number (integer) in order for it to tessellate. Show in the diagram how the builder will lay the floor. On the grid below draw 7 more quadrilateral tessellations.Ī bathroom floor needed to be tiled and the owners left two types of tiles. On the graph show this quadrilateral tessellating at least 5 times.Ĭlick on the image below to reveal the answer.
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