I used to
make these on my
notebooks in high school. I'm so glad there's a node for them. The only thing I feel should be
added is that this
continuing shape (where you draw little triangles out from the middles of the sides of the big one, with their sides 1/3 the length of the original, and then
repeated that operation over and over again) is one of
few examples of an
infinite line enclosing a
finite area. If you draw a
circle around the
original triangle, the continuous figure you end up drawing will never enclose more space than that
circle, and yet the line around the outside of the figure is
infinite in length, as long as you keep
generating it by adding more
little triangles to the sides. It always
approaches the amount of
area tha the circle has, but it'll never
get there. It's
asymptotic.
Thanks for the
node; you got my vote.