Geometry Fractal Project
Due Date _____________________________________
1. Research Sierpinski. List 3 facts and why you think they are important enough to
select.
2. Investigate Sierpinski’s Trangle
a. Draw a large triangle on an 8x10 piece of plain paper; you cannot use an
equilateral triangle. Label it ABC.
b. Measure the angles and sides of the triangle. Classify the triangle by sides
and degrees. Calculate the area and perimeter. Fill in the table provided.
c. Find the midpoints of each side of the triangle. Connect the midpoints
with line segments.
d. Trace one of the triangles onto to worksheet provided. Name the
corresponding vertices A1, B1 and C1.
e. Measure the sides and angles of the traced triangle. Fill in the table
provided.
f. On the original triangle, color the middle, upside down triangle. We will
not be using this one.
g. For each of the remaining triangles repeat c, d,e and f, use A2, B2 and C2
for iteration 2.
h. Repeat c, d, e, f and g for two more iterations.
3. How are the triangles created similar? Use the definition of similar triangles to
show that they are similar. Find the similarity ratio and write it on the worksheet.
4. Create your own fractal.
a. Begin with an initial shape or line segments (called the seed)
b. Write down a rule.
c. Follow the rule for 4 iterations.
d. What do you notice about your fractal?
i. How are the successive shapes similar to the original?
ii. Is the shape getting smaller or larger?
iii. What features of the shape are tending to infinity?
iv. What features of the shape are tending to zero?
Fractal Worksheet
Copies of Sierpinski’s iteration triangles 1, 2, 3 and 4
Table of sides, perimeter and area.
AB
cm
Initial
(Seed)
Iteration 1
Iteration 2
Iteration 3
Iteration 4
BC
cm
AC
cm
Height
cm
Perimeter Area
cm
cm2