![]() It is very important to be mathematically correct with your shape. Once you have your shape, create a stencil from it. Your overall success of your tessellation is built on this shape. This creative stage is the most important part of the assignment. Push yourself to challenge how you are looking at the shape you are developing. It is similar to the composition creativity sheets. Step 1 – make stencil Step 2 – trace and repeatġ0 Assignment Keep playing around with different shapes until a recognizable image can be derived. Any piece you remove must be re attached on the opposite side of your rectangle. To begin working out a new shape, you will remove pieces from your rectangle. To do this you may start your shape with a rectangle or square. One method is to translate a shape across and down to fill the paper. To begin you must first design a shape that will fit together with itself, or another shape, so that your tessellation will have no negative space when you create a pattern with your shape. Its floors, walls, and ceilings are covered with tessellations and other repeating patterns. It is a well-known Islamic architectural marvel which is located in Granada, Spain. The term tessellation comes from the Latin word tessella, meaning tile.ĥ Alhambra Palace, Spain Escher was influenced by the tessellated patterns in the Alhambra palace. A Tessellation is an example of a repeating pattern where shapes fit together in a way that leaves no space in between. In other patterns they may repeat then vary into another form or design. In some patterns a shape is repeated over and over again. Escher died on the 27th of March, He was an amazing artist, and the "King" of Tessellations"Ĥ What is a Tessellation? Patterns are made up of repeating shapes or forms. His fame began to spread in the 1950's, and his work began to be displayed in science museums rather than art galleries. Escher adopted a highly mathematical approach with a systematic study to his art. Escher studied at the School of architecture and Decorative Arts in Haarlem, Netherlands.ģ Who is Escher? However, Escher gave up architecture in favor of graphic arts at the age of 21. He was born on the 17th of June, in 1898, in Leeuwarden, Netherlands (Holland). In the rightmost figure, we used octagons and squares in tiling, which is considered as a semi-regular tessellation.2 Who is Escher? Maurits Cornelius Escher is a very popular artist, and many people recognize his work from posters and calendars. The polygons shown in Figure 7 are some of the tiles which are not regular polygons. We will not limit, of course, our creativity by using only regular polygons in tiling floors. This proves that the only regular polygons that we can use to tessellate the plane are the three polygons shown in Figure 2. ![]() ![]() ![]() Hence, there is no way that we can tessellate the plane with regular polygons having number of sides greater than six. Now, to tessellate, the two adjacent interior angles of these polygons must add up to 360 degrees, which means that each of them must equal 180 degrees. This is because their angle sum would be greater than 360 degrees (we can verify this using the Tessellation GeoGebra applet).Thus, for polygons more than six sides, only two vertices can be placed adjacently without overlapping. Since all regular polygons with more than six sides have interior angles measuring greater than 120 degrees, placing their three interior angles at a common point will make two of them overlap. Consequently, the measure of their exterior angles is 0.įurthermore, observe that as the number of sides of the polygons increases, the fewer the number of vertices that we can fix at a common point without the polygons overlapping. Looking at the table in Figure 6, we can see that polygons whose product of interior angles and the number of adjacent vertices is 360 tessellate. ![]() Figure 6 – Table showing properties of tessellating and non-tessellating polygons. ![]()
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