Sierpinski Triangle


Did you know?
Waclaw Sierpinski lived 1882 to 1969. He was one of the most famous Polish mathematicians. He produced 724 papers and 50 books on the subject of mathematics. Although he lived at a time when the occupying Russians tried to keep the Poles illiterate and generally uninformed, Sierpinski entered the Department of Mathematics and Physics at the University of Warsaw, where he proved to be an outstanding student. Sierpinski received many medals, awards, and honors from the Royal Societies of most of the European nations, and founded several publications.

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are the same at different zoom levels. They are created by repeating a simple process over and over in an ongoing feedback loop. Fractals are fun because they go on forever - they are infinitely complex. The Sierpinski triangle is a fractal described by Waclaw Sierpinski in 1915. It is a self-similar structure that repeats at different levels of magnifications.

The Sirpenski triangle is composed of multiple triangles inside of one triangle. It can grow or shrink by using the same pattern. Its similarity is compared to fractions as the triangle either multiplies or divides itself.

TRY THIS

Materials:

  • Paper
  • Pencil
  • Ruler

Construct a Sierpinski triangle

Draw a large equilateral triangle (an equilateral triangle has three sides the same length and three 60 degree angles)

Find the midpoints of the line segments of the triangle. Then, connect the midpoints, creating smaller triangles.

This pattern is then repeated for the three smaller triangles found in the points of the larger triangle.

Repeat for the three smaller triangles found in the points of these triangles.

And repeat… There are an infinite number of repetitions. How many can you make?

This is called Sierpinski's triangle.

STEP IT UP

Try this with other shapes: divide a square into a 3 X 3 square. Look up Koch’s snowflake.

PARENT & TEACHER TOOLS

This program has been designed for you to share with your child. Read the material together, ask questions and encourage your child to ask questions. Then nurture their curious mind by doing the activities with them. Books included are available via CPL’s digital library (with a library card).