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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:
> [snip]
> 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.