Cyclic Averages of Regular Polygons and Platonic Solids

Authors

  • Mamuka Meskhishvili Department of Mathematics, Georgian-American High School, 18 Chkondideli Str., Tbilisi 0180

DOI:

https://doi.org/10.26713/cma.v11i3.1420

Keywords:

Regular polygon, Platonic solid, Circle, Sphere, Locus, Sum of like powers, Rational distances problem

Abstract

The concept of the cyclic averages are introduced for a regular polygon \(P_n\) and a Platonic solid \(T_n\). It is shown that cyclic averages of equal powers are the same for various \(P_n(T_n)\), but their number is characteristic of \(P_n(T_n)\). Given the definition of a circle (sphere) by the vertices of \(P_n(T_n)\) and on the base of the cyclic averages are established the common metrical relations of \(P_n(T_n)\).

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Published

30-09-2020
CITATION

How to Cite

Meskhishvili, M. (2020). Cyclic Averages of Regular Polygons and Platonic Solids. Communications in Mathematics and Applications, 11(3), 335–355. https://doi.org/10.26713/cma.v11i3.1420

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Section

Research Article