Abstract
We look at the conditions on a center of mass operator, acting on finite sets of mass points (P, m) (with P being the point and m the mass concentrated at P), that entail that the metric of the plane is Euclidean, in the sense that there exists a rectangle, or that the sum of the angles of any triangle is \(180^{\circ }\). It turns out that the independence of the mass concentrated in the center of gravity of a system of two mass points (A, m) and (B, m), of the distance between A and B, even if applied to systems of at most three mass points, implies the Euclideanity of the metric.
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Pambuccian, V. Conditions on centroids implying Euclideanity. Beitr Algebra Geom (2024). https://doi.org/10.1007/s13366-024-00741-2
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DOI: https://doi.org/10.1007/s13366-024-00741-2