Sierpinski’s Triangle

If line segments are drawn between each pair of midpoints of the sides of an equilateral triangle, four smaller congruent triangles are formed. If the middle triangle is removed, the resulting figure represents the first stage in creating Sierpinski’s triangle. If this process is repeated for the three remaining triangles, the second stage for Sierpinski’s triangle is completed. If this process is continued indefinitely, Sierpinski’s triangle is created.

Paradoxically, the area of Sierpinski’s triangle is zero, but the total length of the line segments that form all of the triangles is infinite.

In Chi Hi’s Math Investigations course, students explore these geometric concepts along with other mathematical procedures that create Sierpinski’s triangle.