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Topic: Regular heptagon and angle trisections
Replies: 17   Last Post: Oct 22, 2012 1:34 PM

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Robin Chapman

Posts: 412
Registered: 5/29/08
Re: Regular heptagon and angle trisections
Posted: Oct 10, 2012 4:20 AM
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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.

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