Subject: Re: [HM] Minkowski's ? function and a certain number sequence
From: Peter Flor (peter.flor@kfunigraz.ac.at)
Date: Tue May 30 2000 - 07:33:11 EDT
Minkowski's notation is the reverse from Conway's: ?(x) is dyadic for
rational x, thus: ?(1/3) = 1/4, ?(1/4) = 1/8, ?(2/5) = 3/8 and so on;
generally, ?(x) = x for x=0 and x=1, and, if a/b and c/d are Farey
neighbors, then ?((a+c)/(b+d)) = (?(a/b)+?(c/d))/2. He notes that ?
maps the set of all quadratic irrationals (in [0,1]) monotonically
onto the set of those rationals (again in [0,1]) whose denominator is
not a power of 2.
Best wishes to all, Peter Flor.
This archive was generated by hypermail 2b28 : Tue May 30 2000 - 18:23:53 EDT