These are named after their inventor, English mathematician and theoretical physicist Sir Roger Penrose. Mrs Jaggers year 8 maths classes have been exploring the mathematical art form of tessellation, discovering regular and semi-regular tessellations. In fact, there is a famous family of tessellations based on two tiles known as "Penrose" tiles. A tessellation made up of two or more regular polygons- the pattern at each vertex must be the same. Tessellations do not have to be repeating, or periodic. NB in a semi-regular tessellation, each vertex must have exactly the same shapes in exactly the same order (but can be clockwise or anticlockwise). Repeating and non-repeating tessellations Basically, anytime a surface needs to be covered with units that neither overlap nor leave gaps, tessellations come into play. Examples include floor tilings, brick walls, wallpaper patterns, textile patterns, and stained glass windows. Q: How can you prove that there are only eight semi-regular tessellations A semi-regular tessellation is required to consist of regular polygons, all of the. 301 Tessellation Let us recall what was learnt in Grade 7about tessellation. Tessellations are widely used in human design. Tessellation By studying this lesson, you will be able to, ² identify what regular tessellations and semi-regular tessellations are, ² select suitable polygons to create regular and semi-regular tessellations, and ² create regular and semi-regular tessellations. The three regular and eight semi-regular tessellations are collectively known as the Archimedean tessellations. A semi-regular tessellation is made up of two or more regular polygons that are arranged the same at every vertex, which is just a fancy math name for a corner. There are eight semi-regular tessellations. (A vertex is a point at which three or more tiles meet.) There are only three regular polygons that tessellate in this fashion: equilateral triangles, squares, and regular hexagons.Ī semi-regular tessellation is one made up of two different types of regular polygons, and for which all vertexes are of the same type. Dont tessellate: This is called a semi-regular tessellation since more than one regular polygon is used. Semi-regular tessellations are made up with two or more types of regular polygon which are fitted together in such a way that the same polygons in the same cyclic order surround every vertex.A regular tessellation is one made up of regular polygons which are all of the same type, and for which all vertexes are of the same type. #color(brown)("What are different types of tessellation?"# There are nine different types of semi-regular tessellations including combining a hexagon and a square that both contain a 1-inch side. Using pattern blocks again, have students determine different combinations of two or more regular polygons can be created from. There are only three regular tessellations which use a network of equilateral triangles, squares and hexagons. Semi-Regular Tessellations When two or three types of polygons share a common vertex, a semi-regular tessellation is forms. You can have other tessellations of regular shapes if you use more than one type of shape. A semi-regular tessellation is made using 2 or more types of regularpolygons. Triangles, squares and hexagons are the only regular shapes which tessellate by themselves. Use regular polygons to explore regular and semi-regular tessellations.
#color(brown)("What shapes tessellate and why?"# We may only preserve either the squares or the equilateral triangles, but not both. There are two ways to set this tessellation on hinges. In mathematics, tessellations can be generalised to higher dimensions and a variety of geometries.Ī tiling that lacks a repeating pattern is called "non-periodic". In particular this is what makes it semi-regular: a semi-regular tessellation combines more than one kind of regular polygons, but the same arrangement at every vertex. #color(brown)("What does it mean for a shape to tessellate?"#Ī tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
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