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

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References

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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

Issue

Vol. 11 No. 3 (2020)

Section

Research Article

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