The Sierpinski Triangle

     The work of Waclaw Sierpinski, a Polish mathematician, is now associated with fractal geometry. In 1915 he created what is referred to as the Sierpinski Triangle (Mandelbrot,1977). This triangle demonstrates some of the unusual mathematical concepts that are found in fractal geometry.
   To begin, one must draw an equilateral triangle and then bisect each side. Lines are drawn, connecting the midpoints. A new triangle is formed inside the original creating four triangles within the original. All sides are bisected and joined.

This is a Sierpinski Triangle used as a color wheel by one of my students. 

The amazing fractal think about this triangle is that the length of the perimeters of the triangles are approaching an infinite length while the area approaches zero.