The teacher has the right to drop you one or more levels if your participation and/or work quality is not satisfactory. It will be obvious if you rushed to complete the project at the last minute. Consult the rubric (posted in class) to verify what is required for the project at each level. All required materials will be provided, however you can use your own materials if you prefer. Remember: Finding a design online and copying it is plagiarism and grounds for a zero.Ģ2 Tessellation Project You will have time in class to work on this project. Your design should not look like any of the designs in this presentation. When you have decided on a design, create your template on cardstock. For each seed there is a corresponding region, called. Do not shade Each shape should be different inside. Continue tracing untill yiu fill in the grid. The border around the grid will depend on the paper dimensions (0.5' border for 10'X10' or 1.5' for 12'x12') Trace your first tessellation into the central cell. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). Draw a 9'x9' grid with 3' cells on your paper or board. It can be classified also as a tessellation. Try out several designs, by cutting and taping paper together until you find something you like. In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It will be easiest to perform transformations (for level 2 and above) on regular polygons like the ones below.Ģ1 Suggestions A template that is approximately 2 inches by 2 inches will work well to create an 8 ½ by 11 inch tessellation. Coloring one side of the pattern will help prevent accidental flipping during tracing.Ģ0 Suggestions Polygons that tessellate include regular triangles, hexagons and any quadrilateral (see images below). Note: More than one side may be altered for more challenging designs. You can create more complex designs starting with square tessellations and making changes on both pairs of sides.ġ2 Depending how you decide to color your tessellation, a very simple design can have a very creative result.įor glide reflection tessellations, polygons should have opposite sides that are parallel and congruent – squares, hexagons, parallelograms.ġ4 Example By reflecting and gliding over more than one side, you can create a more complex tessellation.ġ5 Adding coloring and features will enhance the artwork.Īdjacent sides must be congruent – squares, equilateral triangles, regular hexagons, rhombiġ7 Midpoint Rotations Triangles, Squares, and Quadrilaterals One transformation, commonly used to create tessellations is a slide, or translation, of a figure.įor simple translation tessellations, polygons should have opposite sides that are parallel and congruent – squares, hexagons, parallelograms. As you know, transformations are movements of geometric figures. Tessellations can be modified by using transformations. A floor covered by square tiles is an example of a tessellation of squares. Escher’s designs are made from variations on tiling patterns called tessellations. His works look like paintings but were done by woodcarving and lithographs. This is an individual project.Ģ Tessellation Project Maurits Cornelis Escher (1898 – 1972) was a Dutch artist famous for his repetitive, interlocking pattern. You can click and drag the corners of the triangle to change its shape, find the midpoint between two points, and rotate a shape around a point.1 Tessellation Project Today we will discuss the requirements and expectations for your Tessellation projects and you will receive a brief introduction to the different types of tessellations. You might find the interactivity below useful for this: If your answer is yes, can you explain how you know that all triangles tessellate, and can you give an algorithm (a series of instructions) that you can use on any triangle to produce a tessellation? Tessellation Project Maurits Cornelis Escher (1898 1972) was a Dutch artist famous for his repetitive, interlocking pattern. If your answer is no, can you give an example of a triangle which doesn't tessellate and explain why it doesn't? Now try drawing some triangles on blank paper, and seeing if you can find ways to tessellate them. You can print off some square dotty paper, or some isometric dotty paper, and try drawing different triangles on it. You could also draw some triangles using this interactive. Let's think about other triangles which tessellate: We say that a shape tessellates if we can use lots of copies of it to cover a flat surface without leaving any gaps.įor example, equilateral triangles tessellate like this:
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