![]() ![]() To produce a tessellation, you can find the midpoint between two points, rotate a shape around a point, and translate a shape by a given vector. Tessellation, or tiling, is the covering of the plane by closed shapes, called tiles, without gaps or overlaps 17, page 157. You can click and drag the corners of the quadrilateral to change its shape. Example: This tessellation is made with squares and octagons. She’s got a full pictorial tutorial, so check it out 10. A pattern made of one or more shapes: the shapes must fit together without any gaps. You might find the interactivity below useful for this: This binder cover from Indhi Downie features tessellating triangles and will make school work so much more fun She’s gone for a pastel color scheme, but you can use anything. If your answer is yes, can you explain why all quadrilaterals tessellate, and can you give an algorithm which will produce a tessellation of any quadrilateral? Can you explain why it doesn't tessellate? For example, for the first tiling below, each vertex is composed of the point of a triangle (3 sides), a hexagon (6), another triangle (3) and another hexagon (6), so it is called 3.6.3.6. Students cut out a bit from the left side of the index card. They make two cuts and then tape those cuts back onto the notecard. If your answer is no, give an example of a quadrilateral which doesn't tessellate. To start their tessellation project, students create what is basically a puzzle piece. What do you notice about your tessellations? For example, can you find a way to tessellate any parallellogram? What about a kite? Or a trapezium? You might want to think about different types of quadrilaterals. ![]() Have a go at drawing some quadrilaterals, and finding ways to make them tessellate (you can print off some square dotty paper, or some isometric dotty paper, and try drawing different quadrilaterals on it. You could also draw some quadrilaterals using this interactive). What about other types of quadrilaterals? It's quite easy to see how squares tessellate: As another example of ongoing work in finding interesting recreational uses of tilings and patterns, Erik and Martin Demaine, working with Scott Kim and Yushi Uno, released a tiling font in 2021, where each character can be used to tile the plane Citation 2. In this problem we're going to be thinking about tessellating different quadrilaterals. ![]() This problem follows on from some of the ideas in Tessellating Triangles. ![]()
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