Sierpinski’s Triangle on The Geometer’s
Sketchpad® 4.07
Gregg Whisler, Educator
MathScience Innovation Center
Description
In this activity, you will make a classic fractal design. The Geometer’s
Sketchpad® will be used emphasizing transformations and the iterate command.
Materials


Directions
Constructing Simple Single Figures
Computer with The Geometer’s Sketchpad® software installed
Instruction Sheet
1. Open Geometer’s Sketchpad®. A new untitled sketch should appear.
2. Use the line segment tool to construct ∆ABC. Use the labeling tool to name
the points A, B, and C.
3. Use the arrow tool to highlight all three lines. Go to “Construct” and select
“Midpoint”.
4. Use the labeling tool to identify midpoints D, E and F. Your drawing should
look like this:
B
D
A
E
F
C
5. Use the arrow tool to highlight points A, B and C.
6. Go to TRANSFORM – ITERATE. Fill out the dialog box like the following.
Sierpinski’s Triangle on
The Geometer’s Sketchpad® 4.07
http://mathinscience.info
©MathScience Innovation Center, 2007
You can click on the points you want entered in each box of the map rather
than type them.
7. Click on Iterate in the Dialog box. To increase the number of steps, press
”+”, to decrease press”-“.
This is what the final figure looks like.
B
D
A
E
F
C
Constructing Multiple Map Iteration – Sierpinski’s Triangle
1. Start like the last example and stop at STEP 5.
2. Go to “Transform” and choose “Iterate”. Fill out the dialog box like the
following:
3. To make Sierpinski’s triangle, 3 maps are needed. Do you know what they
are? To enter multiple maps from the “Iterate” feature, click on “Structure”
and select “New Map”. Your finished map should look like the one below.
Sierpinski’s Triangle on
The Geometer’s Sketchpad® 4.07
http://mathinscience.info
©MathScience Innovation Center, 2007
4. After clicking on “Iterate” and using the “shift +” to iterate the object
further, Sierpinski’s triangle should appear as shown below.
B
E
D
A
Extensions
C
F

Use The Geometer’s Sketchpad® to add color to your triangles.

Math-History connection. Find information on Waclaw Sierpinski (the
triangle’s namesake).

Fractals Unleashed/Famous Fractals provides a connection to other fractals
the students can create like the dragon fractal and the box fractal.
(http://library.thinkquest.org/26242/full/)

The students may research the Indian art form called Kolam.
http://en.wikipedia.org/wiki/kolam
http://classes.yale.edu/fractals/panorama/art/kolams/kolams.html
Sierpinski’s Triangle on
The Geometer’s Sketchpad® 4.07
http://mathinscience.info
©MathScience Innovation Center, 2007