![]() We do this in GSP by marking our vector as the length of the top of the rectangle in the direction we want the piece to move. Next we cut a particular shape off of one side of the rectangle and paste is to the opposite side. What are properties we know about rectangles? Measure the area of this rectangle. We are going to use our knowledge of geometry and Geometer's Sketch Pad to create our own tessellations.įirst we start with a basic rectangle shape. Artists and mathematicians use the geometry properties that we just learned to create very unique drawings. What observations can you make about rotating an object? If it make a complete rotation, how many degees did the triangle move?Ī Tessellation is a collection of plane figures that fills the plane with no overlaps and no gaps. In our image above, we have rotated the triangle four times to get it back to the original position. If you were to place your thumb in a set position on the desk and move the paper football with your index finger, you would be rotating the football about the fixed point of your thumb. Think about it as a paper football on your desk. In this figure the point of rotation is labeled and that is the point about which the triangle will move. Now we've created a triangle to see what would happen to it if we rotated it. What are some observations you can make about the movement of this figure? In this particular figure, the geometric figure is reflected three times. Figure ABCDE is looking in the mirror at figure A'B'C'D'E. You know how you look in a mirror and the objects you see are backwards? That is exactly how reflection symmetry works. Reflection symmetry is where a figure is reflected over a particular "line of reflection" and the reflected figure is a mirror image of the original. Next we'll create another figure to use in our exploration of reflection. ![]() During this translation the figure stays in the same in the exact same position and it simply move along the line of translation. The diagonal line serves as our "line of translation," it tells us how far and in which direction we will move our figure. Translation essentially means to move from point A to point B. Once we are familiar with the various movements we will create our own Tessellation.įirst we'll create a geometric figure to translate using Geometer's Sketch Pad. In this unit we will explore properties of how different geometric figures move through translation, rotation and reflection. Can you guess how many times a tile would rotate, if each turn were 60 degrees? 45 degrees? 30 degrees? 20 degrees? 15 degrees? Hint: 360 is an important number in geometry.Once students have had the opportunity to explore the various properties of angles and triangles, they can apply their knowledge to look deeper into Transformational Geometry and more specifically, Tessellations. In other rotational tessellations the tile- the basic repeating shape- might rotate 90 degrees four times, and so on. In other rotational tessellations, like the second example at left, a tile might turn 180 degrees, and do it only once.Those pairs of goldfish are turning around their tummies. ![]() In the first example at right, the golfish turns 120 degrees, then does it again, to make three fish in each cluster. We make this tessellation by copying the fish shape and then turning it a little around a point.in this case, where three fishies' back-fins meet. This is the basic "tile" shape of the first goldfish tessellation on this page: it's a goldfish. Rotation (Turning / Spinning) 1 2 3 4 5 6 7
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