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Describing the symmetry of one-dimensional figures by power sums of point coordinates

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Abstract

The article examines the problem of describing the symmetry of a one-dimensional figure by power sums of the coordinates of its points. In case ofn points of unit mass, the figure symmetry requires [(n+1)/2] values of odd power sums; in case of massive points,n values are required in general. A one-to-one correspondence is established between the coordinates ofn points of the figure and the values of power sums to order (2n−1) inclusive.

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Authors
  1. V. S. Levchenkov
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  2. D. V. Levchenkov
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Additional information

Translated from Prikladnaya Matematika i Informatika, No. 2, pp. 106–115, 1999.

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Levchenkov, V.S., Levchenkov, D.V. Describing the symmetry of one-dimensional figures by power sums of point coordinates. Comput Math Model 11, 312–320 (2000). https://doi.org/10.1007/BF02361137

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  • DOI: https://doi.org/10.1007/BF02361137

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