from page 100 of the The Bellini Card by Jason Goodwin
Archimedes was the original Sand Reckoner. I am not quite sure what the above diagram (found here) has to do with Archimedes argument, but it was the best illustration I could find in short order. I found another drawing that points out some interesting features of this diagram, if you are interested. I was hoping to find some pictures of tiles made based on this figure, but no so such luck.