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 dimension Equilateral dimension In mathematics, the equilateral dimension of a metric space is the maximum number of points that are all at equal distances from each other. Equilateral dimension has also been called "metric dimension", but the term "metric dimension" also has many other inequivalent usages. The equilateral dimension of a "d"-dimensional Euclidean space is , and the equilateral dimension of a "d"-dimensional vector space with the Chebyshev distance (L norm) is 2. However, the equilateral dimension of a space with the Manhattan distance (L norm) is not known; Kusner's conjecture, named after Robert B. Kusner, states that it is exactly