Cyclic Averages of Regular Polygons and Platonic Solids

Cyclic Averages of Regular Polygons and Platonic Solids

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 v...

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Veröffentlicht in:Communications in Mathematics and Applications 2020-01, Vol.11 (3), p.335
1. Verfasser: Meskhishvili, Mamuka
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Mathematics
Polygons
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Zusammenfassung: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 \(P_n(T_n)\).
ISSN:0976-5905
0975-8607
DOI:10.26713/cma.v11i3.1420