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Investigation into the progression of patterns in 3d shapes.  

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Borders Coursework I am continuing my investigation into the progression of patterns further, in that, I am no longer working with 2D shapes, but instead 3D ones. I have drawn the first four patterns on separate isometric paper and the pattern number relates to its nth term, i.e. pattern 2 is the same as n = 2. In order to draw the shapes I have drawn them in separate layers, to make it easier to count the total number of squares in each pattern. When drawing each pattern, I added 1 square to each free side of the previous pattern. For instance, pattern 1 is a cube which has 6 sides; therefore I added 6 cubes to it. On the following pages you will see the diagrams that show how the 3D patterns are built up. As shown by my drawings, each pattern's number of layers increases. If we...

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