On quantitative assessment of chirality: right-sided and left-sided geometric objects

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Abstract

Two methods for quantitatively assessing the chirality of a set are considered, the first of which uses the calculation of the area of their symmetric difference of two sets as a measure of the discrepancy between them, and the second uses the Hausdorff distance between them. It is shown that these methods, generally speaking, do not provide a correct quantitative estimate for a fairly wide class of sets, such as bounded Borel sets. Using the example of flat triangles and convex quadrangles, the problem of dividing geometric objects into right-handed and left-handed is considered. For triangles, level lines of two versions of the chirality measure were calculated on the plane of the angular parameters. For a spatial spiral, the values of two versions of the chirality index are found, based respectively on the calculation of the mixed product of vectors and the Hausdorff distance between two sets.

About the authors

Yu. A. Kriksin

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences

Author for correspondence.
Email: kriksin@imamod.ru
Russian Federation, Moscow

V. F. Tishkin

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences

Email: v.f.tishkin@mail.ru

Corresponding Member of the RAS

Russian Federation, Moscow

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