Ethan Siegel of "Starts With a Bang" blog regularly writes excellently on physics topics, but recently did a fine post pertaining more specifically to a geometry puzzle that often winds its way around the Web (...counting the number of triangles within a triangle):
http://scienceblogs.com/startswithabang/2012/07/28/weekend-diversion-triangles-a-puzzle-and-beauty/
a YouTube explanation for the same puzzle is available here:
http://www.youtube.com/watch?v=FxByF38grkQ&feature=player_embedded
Though he doesn't discuss it, Ethan's post actually starts off with a picture of the Sierpinski pyramid, a fractal-based object (which approaches a surface area and volume of 0) that is likely even more fascinating than the puzzle he is elucidating.
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