Newsgroup sci.math 156737

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Angel Garcia wrote:
> 
> Robin Chapman (rjc@maths.ex.ac.uk) writes:
> > In the recent "The Book of Numbers" (Springer 1996) Conway and Guy
> > give constructions for regular 7, 9 and 13-gons using straightedge,
> > compass and angle trisector. The heptagon construction is amazingly
> > neat.
> >
>      Still has not arrived to U of T. I will look for it as soon as
> it arrives.
>    Yes: adding trisection to ruler&compass; makes many classical problems
> feasible. I wonder which type of approximation or method these recent
> Conway and Guy use for trisection.
They present what they call Archimedes's trisection, on p.195.  It
is beautiful.  Assume your ruler has a fixed distance marked upon it.
Draw a circle of that diameter centered at the vertex of the angle to
be trisected.  Extend one side of the angle to be a line A.  Place the
ruler so that it touches the intersection of the circle and the other 
side, and so that one endpoint of the fixed distance touches A.  Move
the ruler keeping those coincidences until the other endpoint of the
fixed distance touches the circle.  A radius from where it touches the
circle to the center makes an angle with the line A that is one
third of the original angle!
D.
mentock@mindspring.com
http://www.mindspring.com/~mentock/index.htm