File talk:Equilateral triangle construction.svg

Alternate formula for area (useful for packing problem)
Note that the area of the triangle formed from drawing a line between 3 nearby circles in a hex packing will have a base of twice the radius and thus the area is r^2*sqrt(3). It is trivial to prove that A) the entire unoccupied area is inside the inner triangle if this larger triangle is broken into 4 equal parts (by drawing lines between centers of each side)  B)  This area is actually even smaller.

Of course, the area of that inner triangle is r^2*sqrt(3)/4 and the sides are the same length as the radius of the circles. 75.70.89.124 (talk) 11:34, 15 August 2013 (UTC)