> // Hi LibraryMan,
> //
> // here is some code for you to play with; the radius of the circles
> // can be specified:
> //
> //    Side * (sqrt(3)-1)/4   circles are mutually touching
> //    Side * sqrt(3)/9       circles intersect in midpoint ("true gothic")
> //    Side * sqrt(3)/6       circles have max. size (all are equal)
> //
> // The distance of the centers (distance AB as named in your link) is
> //
> //    Side-2*sqrt(3)*Radius
> //
> //
> //
> // Sputnik
> //
> //
> // ----------------------------

> // fr### [at] computermuseumfh-kielde
> // ----------------------------
> 
> 
> // +W640 +H480 -F +D +A0.1
> 
> // macro for trefoil ====================================================
> 
> #macro Trefoil (Side, Radius) // lower left corner at origin
> 
>   #local R = 0.005; // "Linewidth"/2
> 
>   #local Height  = sqrt(3)/2*Side;
> 
>   #local Corner1 = <Side/2, Height, 0>; // top corner
>   #local Corner2 = 0; // bottom left corner
>   #local Corner3 = Side*x; // bottom right corner
> 
>   #local Center  = <Side/2, Height/3, 0>; // triangle
> 
>   #local Center1 = <Side/2, Height-2*Radius, 0>; // top circle
>   #local Center2 = <sqrt(3)*Radius, Radius, 0>; // bottom left circle
>   #local Center3 = <Side-sqrt(3)*Radius, Radius, 0>; // bottom right circle
> 
>   union {
>     union {
>       sphere { Corner1, R }
>       sphere { Corner2, R }
>       sphere { Corner3, R }
>       cylinder { Corner1, Corner2, R }
>       cylinder { Corner2, Corner3, R }
>       cylinder { Corner3, Corner1, R }
>       texture { pigment { color green 1 } finish { ambient 1 } }
>       }
>     union {
>       torus { Radius, R rotate 90*x translate Center1 }
>       torus { Radius, R rotate 90*x translate Center2 }
>       torus { Radius, R rotate 90*x translate Center3 }
>       texture { pigment { color red 1 } finish { ambient 1 } }
>       }
>     // "}" omitted to allow application of transformations
> 
>   #end//macro Trefoil
> 
> 
> // simple scene with trefoils ===========================================
> 
> Trefoil ( 1  , 1*(sqrt(3)-1)/4 ) translate <-1.6,  0.2  , 1> } // small
> Trefoil ( 2  , 2*sqrt(3)/9     ) translate <-1  , -1    , 1> } // gothic
> Trefoil ( 1  , 1*sqrt(3)/6     ) translate < 0.6,  0.2  , 1> } // large
> 
> light_source { <-1500, 2500, -2000>, color rgb 1 }
> 
> camera { orthographic up 3*y right 4*x }
> 
> 
> // END ==================================================================
> 
> 
Following up after your explanation about the unintentional personal 
reply, I appreciate your offer to give further explanation.  I realized 
after my original posting of the question that it's theoretically 
possible to have numerous (even infinite?) possibilities for circles 
within a triangle which fit the parameters I mentioned.  The circles 
could be infinitely small and still fit, being tangent to both sides 
surrounding a vertex.
The 2nd configuration you listed, with the radius equal to Side * 
sqrt(3)/9 , was of course the one I had in mind, but how did you figure 
out the math?  Just curious -- I rendered it and it works, sure, so I'm 
not "looking a gift horse in the mouth"
Thanks,
Mark

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