scott <sco### [at] scottcom> wrote:
> >> (L/2)^2 = (S/2 + S*sin(30))^2 + (Scos(30))^2
> >> (L/2)^2 = (S/2 + S/2      )^2 + 3/4*S^2
> >> (L/2)^2 = 7/4 * S^2
> >>    L^2    = 7 * S^2
> >>    L      = sqrt(7) * S
> >
> >
> > You two seem to have a peculiar (to me) way of going about your trig.
> > Either they do it a different and, admittedly, interesting way on "The Other
> > Side of The Pond", than we do here in 'Murica, or -
> > "We" do it weird, or -
> > I just never really learned it very well.
> >
> > I recall going through something like this puzzling out Friederich Lohmueller's
> > pulley/belt calculations with Jerome.
> > You pick what, to me, is the least obvious approach.  :D
> >
> > I'd like to hear and see more about all of this side/2+side*sin(30) business.
> > I did it what seems to me a more direct way, but got the same answer. {whew!}
> > :)
>
> The problem is, assuming the horizontal distance to be S requires you to
> either know that (I didn't) or figure it out from S/2+Ssin(30) or some
> other geometric method.
>
> I think I did it because I have a habit to start from the minimum
> possible number of assumptions, in this case a hexagon has side length S
> and angle 120 degrees. That's enough information to solve it. I've found
> in past situations that faulty assumptions are often what cause errors,
> so I try not to make them if they are not needed.
>
> > See my updated diagram.   Hopefully it's correct - I haven't yet finished coffee
> > #1.
> > I'm going to ponder how this gets converted into code, since there's an ever
> > increasing number of line segments to be drawn at every next level.
>
> Just get the macro to call itself again (with some countdown to prevent
> going forever):
>
> #macro gosper_axiom(p0, p1,N)
>   #if(N>=0)
>      cylinder { p0, p1 0.0078125 }
>      #local V = p1 - p0;
>      #local vT = vnormalize(V);
>      #local len = vlength(V);
>      #local np1=p0+len/sqrt(7)*vec2rot( vT,asin(sqrt(3)/(2*sqrt(7))));
>      #local np2=p1-len/sqrt(7)*vec2rot( vT,asin(sqrt(3)/(2*sqrt(7))));
>
>      gosper_axiom(p0,np1,N-1)
>      gosper_axiom(np1,np2,N-1)
>      gosper_axiom(np2,p1,N-1)
>
>   #end
> #end
>
> Call with eg:
>
> gosper_axiom(<-3,0>,<3,0>,5)
I've tried that. I get "too many nested symbol tables"

More when I'm not posting from my iPod

AB

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