Askold Khovanskii - Center of Mass Technique and Affine Geometry

cm:11527 - Communications in Mathematics, January 3, 2024, Volume 31 (2023), Issue 3 (Special issue: in memory of Sergei Duzhin) - https://doi.org/10.46298/cm.11527
Center of Mass Technique and Affine GeometryArticle

Authors: Askold Khovanskii

    The notion of center of mass, which is very useful in kinematics, proves to be very handy in geometry (see [1]-[2]). Countless applications of center of mass to geometry go back to Archimedes. Unfortunately, the center of mass cannot be defined for sets whose total mass equals zero. In the paper we improve this disadvantage and assign to an n-dimensional affine space L over any field k the (n+1)-dimensional vector space over the field k of weighty points and mass dipoles in L. In this space, the sum of weighted points with nonzero total mass is equal to the center of mass of these points equipped with their total mass. We present several interpretations of the space of weighty points and mass dipoles in L, and a couple of its applications to geometry. The paper is self-contained and is accessible for undergraduate students.


    Volume: Volume 31 (2023), Issue 3 (Special issue: in memory of Sergei Duzhin)
    Published on: January 3, 2024
    Accepted on: October 3, 2023
    Submitted on: July 2, 2023
    Keywords: Mathematics - Metric Geometry,51N10

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