In this project, we learned how to do basic constructions and used them to make beautiful artwork. One of the requirements was to include 8 geometric transformations. The ones that I picked were parallel lines, perpendicular lines, square, octagon, rotation, reflection, translation, and dilation. Because the images were not from my final draft, they are not completely perfect, but my final mandala (pictured left) was very symmetrical and the lines were more parallel. |
My mandala included many parallel lines but the ones in red was one pair of them.
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It also included many sets of perpendicular lines. This means that the lines intersect and form four 90 degree angles.
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Using the set of perpendicular lines and the circles that I drew, I was able to create two perfect squares, one of which is outlined above. This square was not perfect in this draft, but in the final project, it did create a perfect square.
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Though it is not present in my final mandala, when connecting points made bisecting lines, an octagon is formed. This is a regular octagon which means that all side lengths and angle measures are the same.
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This mandala has reflectional symmetry, meaning that if folded in half along the line of symmetry, it would match up perfectly and create a mirror image. All the lines of symmetry are shows above in red and this mandala has a total of 8 lines of symmetry.
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My mandala has level 8 rotational symmetry. This means that every 45 degrees the shape is turned, it will be the same as the original image.
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The next symmetry included in my mandala is translation. One example of translation in this mandala is the circles. These circles are the exact same size, the only difference is one is translated down.
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The final geometric transformation included in my mandala is dilation. My dilation occurs in the shape made by the two squares. One of these shapes is smaller and the other is larger but they are the same shape and proportionate. This means that if the smaller shape was dilated, it would become the same and for that reason, they are symmetrical.
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