Weber problem that, at the optimum, the angles between the AD, BD, and CD straight lines must be equal to 360° / 3 = 120°. Torricelli deduced from that conclusion that: 1– if any triangle ABD, whose ∠ADB angle is equal to 120°, generates an ABDE convex quadrilateral inscribed in a circle, the ∠ABE angle of the ABE triangle must be equal to (180° − 120°)= 60°; 2– one way to determine the set of locations of D for which the ∠ADB angle is equal to 120° is to draw an equilateral ABE triangle (because each angle of an equilateral triangle is
Circle packing in an equilateral triangle removing any single circle from the optimal hexagonal packing of circles. This conjecture is now known to be true for . Minimum solutions for the side length of the triangle: A closely related problem is to cover the equilateral triangle with a fixed number of equal circles, having as small a radius as possible. Circle packing in an equilateral triangle Circle packing in an equilateral triangle is a packing problem in discrete mathematics where the objective is to pack "n" unit circles into the smallest possible equilateral triangle. Optimal solutions are known for "n" < 13 and for any triangular