Take one square piece of paper and cut a weird shape out of one side of the square. Like his other tessellations, Escher began with a geometric tessellation by polygons and worked from there. Make a sketch to show that each polygon in Part a will tile the plane. Start with five squares of paper that are the same size. Escher’s Circle Limit prints are examples of hyperbolic tessellations. The geometric-shaped tile must tessellate itself and fit precisely in the tessellation. Which of the regular polygons tessellated? b. Certain basic shapes can be easily tessellated: squares hexagons triangles Combination shapes, complicated shapes, and animals such as the ones found on these sites are also examples to print and color: Shapes that Tessellate Lizards, M.C. A chessboard is an example of a simple tessellation the squares meet side to side without gaps. What must be true about the measure of an interior angle of a regular polygon in order for the polygon to tessellate? 2. Measure of Sum of the Does the Number of Each Interior Measures of the Angle Angles at P Polygon Angles at P Tessellate? Polygon Triangle Square Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon 1. Continue this process until you have tested each regular polygon. Continue placing triangles edge-to-edge to cover the region around P. Place a vertex of one of the triangles on P. Mark a point P near the center of a separate sheet of paper. Carefully cut out the regular polygons and sort them by shape. For Example: Firstly you need to choose a vertex and then count the number of sides of the polygons that touch it. For example: Which regular polygons will tessellate? To find out, complete the following experiment. There are only three regular tessellations: those made up of squares, equilateral triangles, or regular hexagons. There are many interesting questions related to tessellations. tessella, the Latin word for the small square tiles used in ancient Roman mosaics. For example, equilateral triangles tessellate like this: Lets think about other triangles which tessellate: You can print off some square dotty paper, or some isometric dotty paper, and try drawing different triangles on it. A tessellation is a tiling that uses congruent figures to cover the plane. Regular dodecagons, hexagons, and squares tessellate around. SMP 6, SMP 7 Online: Regular Polygons (Printing the page on card stock works well.) Other: Scissors, tape, a ruler, and five index cards Work individually or in groups of 2 or 3. Regular square and equilateral triangles tessellate around each vertex in the order of 3-3-4-3-4. What is Tessellation A tessellation can be. Ask students to tell you what they know about the word tessellation. Activity 7: Tessellations PURPOSE COMMON CORE SMP MATERIALS GROUPING GETTING STARTED Construct tilings using regular polygons and explore regular and semi-regular tessellations. Examples of tesselations in real life include quilts, mosaic walls and floors, 3D buildings like the Louvre in Paris, and artwork by M.C Escher. Introduce key vocabulary words: tessellation, polygon, angle, plane, vertex and adjacent.
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