7 citations · 12 across the 7 of their papers we have counts for
8 papers
Concentric Circles Each Passing Through One Vertex of Each of Two Regular Polygons
Mamuka Meskhishvili
Given a regular -gon on the plane, it is evident that from any point on the plane, taken as a center, one can draw concentric circles such that each circle passes through on…
Two Regular Polygons with a Shared Vertex
Mamuka Meskhishvili
For two non-congruent regular polygons of the same type, the method of finding the points in the plane at the equal distances to the vertices, is established. The existence of two…
Two Non-Congruent Regular Polygons Having Vertices at the Same Distances from the Point
Mamuka Meskhishvili
For the given regular plane polygon and an arbitrary point in the plane of the polygon, the distances from the point to the vertices of the polygon are defined. We proved that ther…
Cyclic Averages of Regular Polygons and Platonic Solids
Mamuka Meskhishvili
The concept of the cyclic averages are introduced for a regular polygon and a Platonic solid . It is shown that cyclic averages of equal powers are the same for various…
New Sense of a Circle
Mamuka Meskhishvili
New condition is found for the set of points in the plane, for which the locus is a circle. It is proved: the locus of points, such that the sum of the -th powers $S_n^{(2m)}…
Diophantine Equations and Congruent Number Equation Solutions
Mamuka Meskhishvili
By using pairs of nontrivial rational solutions of congruent number equation constructed are pairs of rational right (Pythagorean) triangles with one co…
Parametric Solutions for a Nearly-Perfect Cuboid
Mamuka Meskhishvili
We consider nearly-perfect cuboids (NPC), where the only irrational is one of the face diagonals. Obtained are three rational parametrizations for NPC with one parameter.
Perfect Cuboid and Congruent Number Equation Solutions
Mamuka Meskhishvili
A perfect cuboid (PC) is a rectangular parallelepiped with rational sides whose face diagonals , , and space (body) diagonal are rationals. T…