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
Triangle (musical instrument) form of an equilateral triangle, early instruments were often formed as non-equilateral isosceles triangles. In the early days the triangles did not have an opening and had jingling rings along the lower side. Early examples of triangles include ornamental work at the open end, often in a scroll pattern. Historically, the triangle has been manufactured from a solid iron and later steel rod and bent into a triangular shape roughly equilateral. In modern times, the scroll pattern has been abandoned and triangles are made from either steel or brass. The triangle is often the subject of jokes and one liners