Connect the midpoints of the sides of an equilateral triangle to form 4 smaller equilateral triangles. leave the middle small triangle blank, but for each of the other 3 small triangles, draw lines connecting the midpoints of the sides to create 4 tiny triangles. again leave each middle tiny triangle blank and draw the lines to divide the others into 4 parts. find the infinite series for the total area left blank if this process is continued indefinitely. (suggestion: let the area of the original triangle be 1; then the area of the first blank triangle is 1/4.) sum the series to find the total area left blank. is the answer what you expect? hint: what is the "area" of a straight line? (comment: you have constructed a fractal called the sierpi´nski gasket. a fractal has the property that a magnified view of a small part of it looks very much like the original.)