![]() A semi-regular tessellation is a pattern. There are only three types of regular tessellations, each made from one of the three geometric shapes mentioned above. This means that you can draw a line down the middle of a tessellating shape, and have mirror images. List of convex uniform tilings on Wikipedia. Regular tessellations also have multiple lines of symmetry.(See Semiregular polyhedron on Wikipedia. Conversely, others choose the path of inclusion, admitting figures such as certain nonconvex (but still uniform) star polyhedra, as well as the duals of all included polyhedra. In regard to 3-dimensional polyhedra, convexity is often implicitly assumed, and the infinite classes of prisms and antiprisms may also be omitted, leaving just the Archimedean solids. In geometry, usage is sometimes inconsistent. There are only eight possible semiregular tessellations. The tessellation at the right in Figure 9.38 is not a semiregular tessellation because the two figures are a square and a nonregular octagon. The tessellation at the left in Figure 9.38 is a semiregular tessellation because the two figures are a square and a regular octagon. The Metropolitan Museum of Art: Islamic Art and Geometric DesignĪlso here are links to isometric and square paper.One that we will consider here is the semiregular tessellation-a tessellation of two or more regular polygons that are arranged so that the same polygons appear in the same order around each vertex point. Victoria and Albert Museum: Maths and Islamic Art & Design I encourage you to try creating some of your own tessellations, here are some great resources to get you started! Not only are they visually stunning but they are also rich in mathematics. There is no doubt that there is a lot of sophisticated patterning behind tessellations. Some people claim that all seventeen of these wallpaper groups are represented in the Alhambra Palace in Granada, Spain but it is still being debated. In 1819 Evgraf Stepanovich Fedoro v marked the unofficial beginning of the mathematical study of tessellations when he discovered that every periodic tiling contains one of seventeen different groups of isometrics, now known as wallpaper groups. ![]() Johannes Kepler was one of the first people to study regular and semi-regular tessellations in 1619. Escher was an artist who was famous for creating tessellations that used tiles shaped like animals, humans, or other objects. Irregular tessellations are tessellations made from shapes such as pentagons that are not regular. Semi-regular tessellations are tessellations that use regular tiles of more than one shape with every corner identically arranged. There are only three shapes that can form regular tessellations, equilateral triangles, squares, and regular hexagons. Regular tessellations have both regular tiles and identical regular corners and vertices. There is no denying that these tessellations are masterpieces, but are they mathematical? After some research on tessellations (check out this awesome Wikipedia page!) I have discovered that there are three types of tessellations: regular, semi-regular, and irregular. The Alhambra in Granada, Spain (Google Images)Īlcazar in Sevilla, Spain (Google Images) Here are some famous examples of Islamic tessellations. The Islamic tessellations also included a lot of symmetry, and many designs included translations and rotations of tiles as well. Even though the designs may have only consisted of a couple shapes, the patterns those shapes created couldn't have more variety. The Islamic geometric designs often included a lot of repetition and variations. Therefore Islamic art centers around three main elements: calligraphy in Arabic script, floral and plant-like designs, and geometrical designs. Most interpretations of Islamic law discouraged the portrayal of humans or animals in art for fear that it would cause people to idolize those humans or animals. In order to understand Islamic tessellations, it is important to understand some beliefs of the Islamic faith. The important part though, is that those tiles cannot overlap, nor can there be any gaps between the tiles. So what exactly are tessellations? Tessellations are tilings of the plane using one or more geometric shapes, called tiles. I have been learning such a rich history of mathematics but there is one topic in particular that has stood out to me, Islamic tessellations. Our discussions have ranged from talking about mathematicians such as Archimedes, Brahmagupta, and Leonardo of Pisa (also known as Fibonacci) to talking about the Pythagorean Theorem and arithmetic in Roman numerals. This semester I am taking my capstone class, The Nature of Modern Mathematics, and this class has been pushing the boundaries of what I consider mathematics. The more math I learn the less it fits into the conventional definition I once had of mathematics. ![]()
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