41.
Sample answer: The leaves in the tree and the
branches of the trees are selfsimilar. These self
similar shapes are repeated throughout the
painting.
42a.
The flower and mountain are computer
generated; the feathers and moss are real.
42b.
The fractals exhibit selfsimilarity and iteration.
43.
See students’ work.
44.
In Stage 1, the shaded triangle has legs 3 and
4 units. The hypotenuse has length
c
, where
c
2
3
2
4
2
, or
c
9
16 or 5. So, the
perimeter of the triangle is 3
4
5 or 12 units.
In Stage 2, there are three small shaded triangles
and the larger shaded triangle from Stage 1. Each
of the small shaded triangles has legs 2 and
1.5 units. The hypotenuse has length
d
, where
d
2
2
2
1.5
2
, or
d
4
2.25 or 2.5. So, the
perimeter of all shaded triangles in Stage 2 is
3(2
1.5
2.5)
12 or 30 units.
45.
Sample answer: Fractal geometry can be found in
the repeating patterns of nature. Answers should
include the following.
• Broccoli is an example of fractal geometry
because the shape of the florets is repeated
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Fractal Geometry, Fractal, Sample answer, Selfsimilarity, small shaded triangles

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