Fractals
Begin with a square (try a 9 x 9 square on square dot paper).
Trisect each side, then construct a new square on the center section,
making a figure consisting of 20 sides.
Repeat the process, trisecting each of the 20 sides, and
constructing squares on the middle sections, thus forming a polygon
of 100 sides. Repeat the process on to infinity.
What is the perimeter and the area of the polygon?
Fill in the chart below for each stage of the polygon (up to stage five).
# of
Stage sides length perimeter area
----- ----- ------ --------- ----
1 4 a 4a a^2
2 _____ ______ _________ ____
3 _____ ______ _________ ____
4 _____ ______ _________ ____
5 _____ ______ _________ ____
n _____ ______ _________ ____
Now examine the chart on the next
page to check your work.