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
Equilateral triangle area of all those circumscribed around a given circle is equilateral. The ratio of the area of the incircle to the area of an equilateral triangle, formula_30, is larger than that of any non-equilateral triangle. The ratio of the area to the square of the perimeter of an equilateral triangle, formula_31 is larger than that for any other triangle. If a segment splits an equilateral triangle into two regions with equal perimeters and with areas "A" and "A", then If a triangle is placed in the complex plane with complex vertices "z", "z", and "z", then for either non-real cube