Re: construction with rule and compass by John Conway

Subject:      Re: construction with rule and compass
Author:       John Conway
Date:         Dec 14 14:21:20 1995

On Thu, 14 Dec 1995, gao s wrote:

> Does anybody know references on algorithms of deciding whether a
> geometric configuration can be constructed with ruler and compass, or
> equivalently, whether a set of algebraic equations can be solved with
> +, -, *, /, and square roots. 
> Thank you very much,
> X.S. Gao
> Computer Science Department
> Wichita State University

    This is equivalent to asking whether its Galois group (over
the field generated by the coordinates of the points and lines
involved) is a 2-group.  

    There ARE algorithms to work out Galois groups, but they
usually only work for equations of fairly low degree, and have 
often been implemented only over the rationals.  

   John Conway

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