Explore Sierpinski's Triangle 1

Making Sierpinski's Triangle Let's create a shape: Begin with an equilateral triangle. Divide the triangle into four equal smaller equilateral triangles. Remove the middle triangle, leaving the three remaining triangles touching at the corners. Repeat steps 2 and 3 for each triangle left behind. Continue to repeat, ad infinitum. To see this in action, press the "Start" button to the right. This amazing shape is known as the Sierpinski Triangle, named after Wacław Sierpiński (1882 - 1969), a Polish mathematician who invented and studied it. The Sierpinski Triangle is an example of a fractal, a shape that has scaling symmetry. Most people are used to three types of symmetry - translation, rotation and reflection - which work by taking a shape and "moving" it in a certain way, then comparing the moved version to the original version. If the two versions cannot be told apart, the shape is said to be symmetrical. Scaling symmetry works the same way. However, instead of "moving" the shape, we make it larger or smaller. If the large version (or a piece of it) looks the same as the small version, the shape is said to be scaling symmetrical. Take a detour to Area Of Sierpinski's Triangle. Take a detour to Fractal Gaskets. Continue with Explore Sierpinski's Triangle.