| Pauling's Revenge |
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Dear Friends I'm sorry that I have to miss this manganese jubilee. Ron was mumbling something about silver when he invited me, apparently forgetting that manganese holds position 25 in the aperiodic table. The old-timers, of course, will remember that it was manganese that started the whole thing. It would have been fun to catch up on developments. Are we any closer to a resolution of the fundamental question — entropy or energy? Although I have not been active in this area lately, here is a true story to show that quasicrystals will remain a part of my past that I can never escape. Earlier this sumer I was attending a conference on optimization at MacMaster University in Hamilton, Ontario. Seeing the campus reminded me of my only other visit to Hamilton: a crystallography meeting in 1986 where I shared the podium with Linus Pauling. The great man's spirit seems to have found a home in this Canadian city, at least that would explain the strange dream I had there. In this dream I was visited by 25 colored tiles, shown above on the left. In spite of their square shapes, these tiles have a profound 5-fold symmetry in the following sense. Permute the 5 colors cyclically, purple → blue → green → yellow → red → purple and the set of tiles is unchanged! Naturally I interpreted the colors as matching rules and, as you might have guessed by now, the question foremost in my mind was whether the infinite plane could be tiled. The (incomplete) effort shown above on the right would have appealed to Pauling: a periodic tiling that uses all 25 tiles of the set within a 5 × 5 unit cell. Is it possible? Was Pauling right after all? If this interests you — and how could it not — print out the sheet of tiles on a color printer, apply to a thin piece of cardboard with a glue stick, and cut out the squares with scissors. Happy tiling! Veit Elser |
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