OFFTOPIC: Fermat numbers (was Re: Numerical language ...)
|From:||Carlos Thompson <chlewey@...>|
|Date:||Thursday, November 19, 1998, 1:19|
Didier Willis wrote:
> Douglas Koller wrote:
> > Nik Taylor wrote:
> Beside 2, constructible numbers (that is divisions of a circle that may be
> constructed with a pair of compasses and a ruler) are prime Fermat numbers and
> their multiples (The theorem was proven by the mathematician Gauss -- There
> many other interesting things about Fermat numbers, but it would be really too
> off-topic here. I may just add that very few Fermat numbers are prime, though
> the first ones all appear to be prime).
Actually there are infinity of prime Fermat numbers, but density is very low.
> Fermat numbers are of the form (2^2^a + 1), e.g. 3, 5, 17, 257...
> Incidentally, 17 (2^2^2 + 1) is constructible, so there is a
> method (though quite complex, and presumably really too complex
> for Old Babilonians:) to divise a circle in 17 exact parts with
> a pair of compasses and a ruler.
I've somewhere read that in the safe box of some University in USA is stored the
method for constructing a regular 257 sided poligon with compasses and ruler.