![]() ![]() On the tracing paper we draw around the shape and mark the centre of rotation We can use tracing paper to rotate a shape The fixed point is called the centre of rotation.Įxample: Rotate shape A 180° about centre (1,1) We can now move this point 5 right and then 2 up.įrom this point we need to draw a shape that is the same as shape A.Ī rotation turns a shape around a fixed point. We can start by picking a point on shape A. Means we need to move the shape 5 right and 2 up ![]() The transformation is a translation by the vector We can write 6 left and 5 up as a vector: We have a translation 6 to the left and 5 up. Next we look at how far to move in the up or down direction: We can now look at how far we need to move to get from the point on A to the same point on Bįirstly we look at the left or right direction: To find out how much the shape has moved we need to pick a point on shape A and find the same point on shape B. We put a set of brackets around these numbers.Ī movement to the right is positive and a movement to the left is negative.Ī movement up is positive and a movement down is negative. We write the left/right movement on top of the up/down movement. We can describe a translation using a vector. The transformation that maps shape A onto shape B is a translation 4 right and 3 up. Now we can look at how far up or down to move. We start by looking at how far to move left or right. If we take the bottom right corner of A we have to see how far we have to move the to get to the bottom right corner of B. We need to know how far to move left/right and how far to move up/down. We can take any point of shape A and see how far we have to move to get to the same point on shape B. We also need to know by how much the shape has moved. This transformation is called a translation We can see that the shape has moved and all points have moved by the same amount. All points of the shape must be moved by the same amount.Ī translation can be up or down and left or right.Įxample: Describe the transformation that maps shape A onto shape B Lizard tiles by Ben Lawson.A translation moves a shape. Hexagonal and rhombic tessellations from Wikimedia Commons. Triangular tessellation from pixababy.If you want to try a more complicated version, cut two different squiggles out of two different sides, and move them both.Color in your basic shape to look like something - an animal? a flower? a colorful blob? Add color and design throughout the tessellation to transform it into your own Escher-like drawing. The shape will still tessellate, so go ahead and fill up your paper.Then move it the same way you moved the squiggle (translate or rotate) so that the squiggle fits in exactly where you cut it out. On a large piece of paper, trace around your tile. Tape the squiggle into its new location.It’s important that the cut-out lines up along the new edge in the same place that it appeared on its original edge.You can either translate it straight across or rotate it. Cut out the squiggle, and move it to another side of your shape.Draw a “squiggle” on one side of your basic tile.The first time you do this, it’s easiest to start with a simple shape that you know will tessellate, like an equilateral triangle, a square, or a regular hexagon. Here’s how you can create your own Escher-like drawings. Tessellations are often called tilings, and that’s what you should think about: If I had tiles made in this shape, could I use them to tile my kitchen floor? Or would it be impossible? The first two tessellations above were made with a single geometric shape (called a tile) designed so that they can fit together without gaps or overlaps. So we’ll focus on how to make symmetric tessellations. It’s actually much harder to come up with these “aperiodic” tessellations than to come up with ones that have translational symmetry. The Penrose tiling shown below does not have any translational symmetry. Many tessellations have translational symmetry, but it’s not strictly necessary. The idea is that the design could be continued infinitely far to cover the whole plane (though of course we can only draw a small portion of it). \)Ī tessellation is a design using one ore more geometric shapes with no overlaps and no gaps. ![]()
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