41.Sample answer: The leaves in the tree and thebranches of the trees are self-similar. These self-similar shapes are repeated throughout thepainting.42a.The flower and mountain are computer-generated; the feathers and moss are real.42b.The fractals exhibit self-similarity and iteration.43.See students’ work.44.In Stage 1, the shaded triangle has legs 3 and4 units. The hypotenuse has length c,where c2532142, or c5Ï9116wor 5. So, theperimeter of the triangle is 31415 or 12 units.In Stage 2, there are three small shaded trianglesand the larger shaded triangle from Stage 1. Eachof the small shaded triangles has legs 2 and1.5 units. The hypotenuse has length dd252211.52, or d5Ï412.w25wor 2.5. So, theperimeter of all shaded triangles in Stage 2 is 3(211.512.5)112 or 30 units.45.Sample answer: Fractal geometry can be found inthe repeating patterns of nature. Answers shouldinclude the following.
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.