File talk:Equilateral triangle construction.svg
Latest comment: 11 years ago by 75.70.89.124 in topic Alternate formula for area (useful for packing problem)
Alternate formula for area (useful for packing problem)
editNote 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)