This preview shows page 1. Sign up to view the full content.
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
5
3
2
1
4
2
, or
c
5
Ï
9
1
16
w
or 5. So, the
perimeter of the triangle is 3
1
4
1
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
d
2
5
2
2
1
1.5
2
, or
d
5
Ï
4
1
2.
w
25
w
or 2.5. So, the
perimeter of all shaded triangles in Stage 2 is
3(2
1
1.5
1
2.5)
1
12 or 30 units.
45.
Sample answer: Fractal geometry can be found in
the repeating patterns of nature. Answers should
include the following.
This is the end of the preview. Sign up
to
access the rest of the document.
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.
 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Fractal Geometry

Click to edit the document details