On 10/10/2012 06:44, Bill Taylor wrote: > I've been bobbling through Ian Stewart's > > ** "A Cabinet of Mathematical Curiosities", > > (which I firmly recommend, BTW, along with his other books), > when I came across a remark that, although a regular heptagon > is not constructible with ruler and compass only, it IS > constructible if you add in an angle-trisecting device! > > Well, that sounded fun, as trisections seem to have little to do > with heptasections, on the face of it. No further details or > references were given, but I soon managed to convince myself, > using basic Galois ideas and complex numbers, that it would be > possible, in principle. (That's the 1st exercise for the reader!) > > However, it would be a pretty hopeless mess to try to convert > that algebra into a neat geometric construction, so there is > my main query, (and thus 2nd exercise for the reader...) > > ** Find a simple geometric construction of a regular heptagon > ** using ruler, compass and angle-trisector.
See Conway and Guy's "The Book of Numbers". They also do the regular 13-gon.