Question

What is Seirpinski’s Triangle?
(about 100-150 words)​

Answer 1

Answer:

The Sierpinski triangle is a fractal described in 1915 by Waclaw Sierpinski. It is a self similar structure that occurs at different levels of iterations, or magnifications. We can use Geometer's Sketchpad to construct these types of triangles, and then compare them to the pattern of Pascal's Triangles.

Below, a pattern has begun by finding the midpoints of the line segments of the largest triangle. Then, by connecting these midpoints smaller triangles have been created. This pattern is then repeated for the smaller triangles, and essentially has infinitely many possible iterations. This is called Sierpinski's triangle.

The Sierpinski triangle generates the same pattern as mod 2 of Pascal's triangle. That is to say, the even numbers in Pascal's triangle correspond with the white space in Sierpinski's triangle. In fact, Pascal's triangle mod 2 can be viewed as a self similar structure of triangles within triangles, within triangles, etc.