![]() ![]() 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. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.The more math I learn the less it fits into the conventional definition I once had of mathematics. Tessellations are sometimes employed for decorative effect in quilting. Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the Moroccan architecture and decorative geometric tiling of the Alhambra palace. ![]() Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor, or wall coverings. A tessellation of space, also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions.Ī real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern. A tiling that lacks a repeating pattern is called "non-periodic". The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged. An example of non‑periodicity due to another orientation of one tile out of an infinite number of identical tiles.Ī periodic tiling has a repeating pattern. ![]()
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