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arXiv · 2010.12340

Cyclic Averages of Regular Polygons and Platonic Solids

Mamuka Meskhishvili
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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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Mamuka Meskhishvili. 2020-10-22. Cyclic Averages of Regular Polygons and Platonic Solids. https://doi.org/10.26713/cma.v11i3.1420

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