English

Cyclic Averages of Regular Polygons and Platonic Solids

General Mathematics 2022-06-22 v1

Abstract

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

Keywords

Cite

@article{arxiv.2010.12340,
  title  = {Cyclic Averages of Regular Polygons and Platonic Solids},
  author = {Mamuka Meskhishvili},
  journal= {arXiv preprint arXiv:2010.12340},
  year   = {2022}
}