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21. Given:
n
ABC
is equilateral.
CD
5
}
1
3
}
CB
and
CE
5
}
1
3
}
CA
Prove:
n
CED
,
n
CAB
Proof:
22.
23.
Yes; the smaller and smaller details of the shape
have the same geometric characteristics as the
original form.
24.
Stage 1: 6
Stage 2: 36
25. Stage
Number of Segments
Pattern
014
0
144
1
21
64
2
36
44
3
The formula is 4 to the power of the stage
number:
A
n
5
4
n
.
So in Stage 8 there are 4
8
5
65,536 segments.
26.
Stage 0: 1 unit, Stage 1:
}
1
3
}
unit, Stage 2:
}
1
9
}
unit,
Stage 3:
}
2
1
7
}
unit; as the stages increase, the
length of the segments will approach zero.
27.
Stage 0: 3 units, Stage 1: 3
? }
4
3
}
or 4 units, Stage 2:
3
1
}
4
3
}
21
}
4
3
}
2
5
3
1
}
4
3
}
2
2
or 5
}
1
3
}
units, Stage 3: 3
1
}
4
3
}
2
3
or
7
}
1
9
}
units
28.
P
5
3
1
}
4
3
}
2
n
; as the stages increase, the
perimeter increases and approaches infinity.
29.
The original triangle and the new triangles are
equilateral and thus, all of the angles are equal to
60. By AA Similarity, the triangles are similar.
30.
The numbers converge to 1.
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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.
 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Angles

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