VM> W[]oops, for (1) I meant that for -pi/2 <= x <= pi/2, that |sin(x)| >= |x| or that |sin(x)| >= pi || x/pi || for *all* real x. The rest of what I said follows without change. <VM Isn't this *still* backwards? I.e., For -pi/2 <= x <= pi/2, |sin(x)| <= |x|. WDS> Returning to pi, http://mathworld.wolfram.com/IrrationalityMeasure.html indicates pi has a most a finite set of rational approxs p/q with |pi-p/q| < q^(-7.7). Therefore, in view of limit(N-->oo) N^(7.7/N)=1, the limit exists and is 1. <WDS Can someone confirm or correct this rephrasing?: "For every r>1 and q> 7.7, the nth term of π's continued fraction exceeds r^q^n at most finitely often." In any event, this is pathetically lame, since we probably only need q>1. --rwg REPHRASING SPRINGHARE RANGERSHIP