Concentric Circles Each Passing Through One Vertex of Each of Two Regular Polygons
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917412809474048 |
|---|---|
| author | Meskhishvili, Mamuka |
| author_facet | Meskhishvili, Mamuka |
| contents | Given a regular $n$-gon on the plane, it is evident that from any point on the plane, taken as a center, one can draw $n$ concentric circles such that each circle passes through one of the vertices of the polygon. Naturally, this raises the problem of whether such a construction is possible for any two given regular $n$-gons on the plane. In this paper, we establish the necessary and sufficient conditions for the existence of $n$ concentric circles such that each circle passes through one vertex of each of the two regular $n$-gons.
Keywords and phrases: Polygonal distances, cyclic averages, concentric circles, two regular polygons, two equilateral triangles, two squares |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14253 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Concentric Circles Each Passing Through One Vertex of Each of Two Regular Polygons Meskhishvili, Mamuka General Mathematics 51M15, 51N20, 51N35 Given a regular $n$-gon on the plane, it is evident that from any point on the plane, taken as a center, one can draw $n$ concentric circles such that each circle passes through one of the vertices of the polygon. Naturally, this raises the problem of whether such a construction is possible for any two given regular $n$-gons on the plane. In this paper, we establish the necessary and sufficient conditions for the existence of $n$ concentric circles such that each circle passes through one vertex of each of the two regular $n$-gons. Keywords and phrases: Polygonal distances, cyclic averages, concentric circles, two regular polygons, two equilateral triangles, two squares |
| title | Concentric Circles Each Passing Through One Vertex of Each of Two Regular Polygons |
| topic | General Mathematics 51M15, 51N20, 51N35 |
| url | https://arxiv.org/abs/2604.14253 |