# Fun with Sierpinski triangle

*“Geometry is nothing at all, if not a branch of art!”* This activity will demonstrate the fundamentals of fractals - how a pattern can repeat again and again at different scales and how a complex shape can be formed by simple repetition. Kids will draw their very own fractal triangle composed of smaller and smaller size triangles.

## Background:

Making a Sierpinski triangle will teach precision. They will learn to analyze and compare shapes based on their properties. It will enable them to create a complex pattern by repeating a simple process over and over again. They will also gain experience to use the mathematical tools strategically along with enjoying it by making such a structure.

## Requirements:

Colored pencils

White Paper

Ruler

## Steps:

Draw a big triangle on the white paper using the edges of the paper. Triangle should point up

Mark the midpoints of the sides of the triangle and draw another triangle using those three midpoints and this triangle should point downwards

Color the triangle pointing downwards with your pleasing color

Now, you have three white triangles

Find the midpoints of each of these three white triangles, connect them, and color them with a different color in the resulting downward-pointing triangles

Now, you have nine small white triangles

Connect the midpoints of each of the nine white triangles to form 27 smaller downward-pointing triangles and color those with a different color

You can continue this process as long as you like

## Learning Opportunity:

This process keeps creating triangles in a factor of 3: 81, 243, …

The Sierpinski triangle, also called the Sierpinski gasket, is a fractal, named after Waclaw Sierpinski

A Sierpinski triangle is a mathematically generated pattern in which self-similar shapes are repeated across different scales in a never-ending feedback loop

It is an infinite process and is not dependent upon the starting shape. YOu can use other shapes as well to understand fractals in a similar fashion