![]() ![]() Octagons and squares can be arranged to form a semi-regular pattern: The image that we are likely to think of is known as a regular tessellation, where all the shapes are regular and of the same type, for example:Ī semi-regular tessellation is made up of two different regular shapes and each vertex (i.e. Traditionally, the pattern formed by a tessellation is repetitive. Two people have principally been responsible for investigating and developing tessellations: Roger Penrose, an eminent mathematician, and the artist, M.C.Escher. Tessellations are a common feature of decorative art and occur in the Presumably this is an indication of the fact that tiles of this shape are the easiest to interlock. The word tessellation itself derives from the Greek tessera, which is associated with four, square and tile. Tessellation is a system of shapes which are fitted together to cover a plane, without any gaps or overlapping. And of course, there is so much maths involved! It seems a golden opportunity to link art with maths, allowing the creative side of your children to take over. There is so much scope for practical exploration of tessellations both For many, this is their preferred method of learning and, in general, it engages pupils more effectively. So often in the classroom we try to make activities more enjoyable for the children by varying our teaching to include a more tactile or "hands on" approach. The Official M.C.'Why tessellation?' you may well be asking.Once students have the program, they can use SketchUp without an Internet connection but the most useful help guides are online. Orbit, Pan and Zoom tools are used for changing viewing angles.Ī free version of SketchUp is available for download from Trimble. The main tools used to construct the tessellations are as follows: Ruler, Select, Move, Draw, Polygon, Protractor, and Paint Bucket tools, and Copy and Paste commands. As yet, no tutorial has been made for constructing a tessellated polyhedron.Īs previously mentioned, a minimal amount of SketchUp tools is needed to complete the activity however, you should become well acquainted with the program before using it for instruction. Even with borrowing ideas from Escher, this was extremely difficult to make. ![]() See the Four Color Map Problems lesson on the Exploratory Lesson’s page for similar exercises. This is a Four Color Map problem, that is - the cube can be colored in such a way that only four colors are needed and no colored region shares a border with the same color. Additionally, a file that contains a cube with a tessellated pattern is available as a download. I’ve also included some tessellation samples and some blank versions for younger grades to color. The file could be used an instructional tool or for self-directed learning. Slide, rotate around a midpoint, and rotate around a vertex transformations are demonstrated in a series of SketchUp scenes. The main download attached is a tutorial on how to perform several transformations in SketchUp. And finally, SketchUp can be used to illustrate how area and perimeter is preserved in the shapes. The Rotation needs to be rotated by measured degrees and so on. With SketchUp, the mathematical concepts are recognized and applied. One only needs to grab a point and drag and the transformation is effected. Additionally, some of the other tessellation applications do all of the work for the user. When students become comfortable with the program then they will be ready for bigger and better things. Only a limited use of the full tool kit is necessary. First, this is a good introduction to the SketchUp application. There are numerous applications available for students to construct tessellations with, but using SketchUp to perform the task has several advantages. SketchUp is a free 3-D modeling application from Google, but it can also be applied for two-dimensional drawings as well. You don’t need to be a strong math student or artistic to create an interesting design. This activity takes students through the steps of using three different types of trans-formations to construct tessellated patterns. A simple tessellation can be seen in a tiled floor but one full of transformations can truly be a work of art. Tessellation is a math topic that is usually found off the beaten path but they contain important geometry and measurement concepts. Explore and apply combinations of transformation and color patterns using SketchUp's tools.Demonstrate translations: slide, rotation around a midpoint, and rotation around a vertex.Construct tessellated patterns using SketchUp. ![]()
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