This was brought to my attention today, and I haven't had much time to think about it; I think it has something to do with fractals. If you have half a circle with diameter of 2, the circumference will be [tex]\pi[/tex]. If you create two circles, each with diameter of 1, the combined length of the circumference is also [tex]\pi[/tex], and the sum of their diameters will remain at 2. If you continue in this fashion, the sum of the circumferences will remain at [tex]\pi[/tex] until the semicircles become points, at which point the sum of the circumferences remains at [tex]\pi[/tex], but the is now the line segment which was the diameter that should actually measure 2 (because the semicircles become points). Can anyone explain?