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Serious Fun with Fractals

November22

fractal foundationThe Fractal Foundation has put together some great resources on this intriguing topic. They note, “We can find fractals all over the natural world, from tiny patterns like seashells up to the giant spirals of the galaxies. Trees, river networks, mountains, coastlines, lightning bolts, blood vessels, flowers, etc are all examples of natural fractals. We can look at a fractal as a picture that tells a story of the natural processes that formed it.” Their site includes an online fractal course which was developed by the Fractal Foundation under a grant from the NM Public Education Department. There seem to be a couple of things to iron out in the demos but this would make a great project for high school Mathematics, especially as it connects to the real world so strongly, such as branching in trees:
fractals_1

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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