Similarly, for F2, since the middle third of each side of F1 is removed and replaced with two line segments, the number of sides in F2 is given by: (fil this box)
Similarly, for F2, since the middle third of each side of F1 is removed and replaced with two line segments, the number of sides in F2 is given by: (fil this box)
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter4: Quadrilaterals
Section4.3: The Rectangle, Square, And Rhombus
Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...
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Question
Solve and fill the blanks in "The Second Hint" and "The Third Hint"
Transcribed Image Text:ACTIVITY : FINDING AREA OF KOCH SNOWFLAKE
Figure 5.11 The first four figures, Fo, F1, F2, and F3, in the construction of the Koch snowflake.
2. THE FIRST HINT
Let Nn denote the number of sides of figure Fn. Since Fo is a triangle, No = 3.
Let In denote the length of each side of Fn. Since Fo is an equilateral triangle
with sides of length lo = 1, we now need to determine N1 and /1. Since F1 is
created by removing the middle third of each side and replacing that line
segment with two line segments, for each side of Fo, we get four sides in F1.
Therefore, the number of sides for F1 is
N1 = 4.3.
3. THE SECOND HINT
Since the length of each of these new line segments is 1/3 the length of the line segments in
Fo, the length of the line segments for F1 is given by
1
%3D
Similarly, for F2, since the middle third of each side of F1 is removed and
replaced with two line segments, the number of sides in F2 is given by: (fill
this box)
48
4. THE THIRD HINT
Since the length of each of these sides is 1/3 the length of the sides of F1, the length of each
side of figure F2 is given by
1/9
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