Re: [math-fun] Pisot & Salem numbers

Each Pisot number arises as a limit point (and from both sides) of Salem numbers. But yes to JA: I should have excluded (or included, anyhow said something special about) Pisot numbers when I was writing that characterization of Salem numbers. Siegel also showed the 2nd smallest Pisot number was 1.38027756 obeying x^4=x^3+1. Apparently it is not known whether the Pisot numbers are the full set of Salem limit points, or whether there are more. Also, amazingly enough, it is known the Pisot numbers are a closed set. It seems clear Pisot and Salem numbers have a lot to do with both recursive tilings and quasicrystals. But I certainly do not fully understand any of these things.