INVALID_ADDRESS wrote:

>Now look at the midpoint 'Center2' of a circle touching the sides
>emanating from Corner2. Due to symmetry of this circle and the triangle
>with respect to the line through Corner2 and Center2, the angle between
>this line and the x-axis is 30 degrees (60/2). Now imagine a new point:
>the mirror image 'M' of Center1 with respect to the x-axis. The triangle
>   Corner2 -- Center1 -- M
>has 30+30 degrees at Corner1 (x-axis symmetry),

I was following just fine until this point (no pun intended).
On *my* diagram, Center1 corresponds to Corner1, Center2 to Corner2, etc.
I wondered if perhaps you meant to say that the point 'M' was the mirror
image of Center2, rather than Center1.  If I make point 'M' a mirror image
(with respect to the x-axis) of Center1, I end up with an isosceles
triangle whose longest side is the vertical line Center1 -- M .  This
leaves me with point 'M' having a y-value which is the negative of


The only way I can come up with the equilateral triangle you reference is by
substituting one vertex so that the vertices of the triangle are now
Corner2 -- Center2 -- M.
(Please forgive crude "drawing"):


| <-- y-axis
|        (.) Corner1
|
|        (.) Center1
|
|   (.)Center2
|
..Corner2______________  (x-axis)
|
|
|   (.) 'M'
|
|
|

Maybe I'm being dense in the head?....
Thanks,
mark

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