Two Non-Congruent Regular Polygons Having Vertices at the Same Distances from the Point
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 there is one more non-congruent regular polygon having the vertices at the same distances from the point. The sizes of both...
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| creator | Meskhishvili, Mamuka |
| description | 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 there is one more non-congruent regular polygon having
the vertices at the same distances from the point. The sizes of both regular
polygons are uniquely determined by these distances. In general case,
geometrical construction of the second regular polygon is given. It is proved
that there are two points in the plane, which separately have the same set of
the distances to the vertices of two non-congruent regular polygons with a
shared vertex. |
| doi_str_mv | 10.48550/arxiv.2201.07974 |
| format | Article |
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the polygon, the distances from the point to the vertices of the polygon are
defined. We proved that there is one more non-congruent regular polygon having
the vertices at the same distances from the point. The sizes of both regular
polygons are uniquely determined by these distances. In general case,
geometrical construction of the second regular polygon is given. It is proved
that there are two points in the plane, which separately have the same set of
the distances to the vertices of two non-congruent regular polygons with a
shared vertex.</description><identifier>DOI: 10.48550/arxiv.2201.07974</identifier><language>eng</language><subject>Mathematics - General Mathematics</subject><creationdate>2022-01</creationdate><rights>http://creativecommons.org/licenses/by-nc-sa/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2201.07974$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2201.07974$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Meskhishvili, Mamuka</creatorcontrib><title>Two Non-Congruent Regular Polygons Having Vertices at the Same Distances from the Point</title><description>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 there is one more non-congruent regular polygon having
the vertices at the same distances from the point. The sizes of both regular
polygons are uniquely determined by these distances. In general case,
geometrical construction of the second regular polygon is given. It is proved
that there are two points in the plane, which separately have the same set of
the distances to the vertices of two non-congruent regular polygons with a
shared vertex.</description><subject>Mathematics - General Mathematics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj71OwzAYRb0woMIDMNUvkOC4dmyPKPwUqSoVjWCMvsR2sJTYyHELfXtoYLi60hmOdBC6KUjOJOfkFuK3O-aUkiInQgl2id7rr4C3wWdV8H08GJ_wq-kPA0S8C8OpD37Cazg63-M3E5PrzIQh4fRh8B5Gg-_dlMCfqY1hnPkuOJ-u0IWFYTLX_79A9eNDXa2zzcvTc3W3yaAULOMcrKVSKq6NtUCUVKQtqQLeSaYYMN1xKouybLX-HW-FsURoUxjNhaJ8tUDLP-1c1nxGN0I8NefCZi5c_QCEmEw0</recordid><startdate>20220117</startdate><enddate>20220117</enddate><creator>Meskhishvili, Mamuka</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220117</creationdate><title>Two Non-Congruent Regular Polygons Having Vertices at the Same Distances from the Point</title><author>Meskhishvili, Mamuka</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-55aff28895deffa09890b629a5c8494a4dc528166bdd6bd5b7ef07de1ed579253</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - General Mathematics</topic><toplevel>online_resources</toplevel><creatorcontrib>Meskhishvili, Mamuka</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Meskhishvili, Mamuka</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two Non-Congruent Regular Polygons Having Vertices at the Same Distances from the Point</atitle><date>2022-01-17</date><risdate>2022</risdate><abstract>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 there is one more non-congruent regular polygon having
the vertices at the same distances from the point. The sizes of both regular
polygons are uniquely determined by these distances. In general case,
geometrical construction of the second regular polygon is given. It is proved
that there are two points in the plane, which separately have the same set of
the distances to the vertices of two non-congruent regular polygons with a
shared vertex.</abstract><doi>10.48550/arxiv.2201.07974</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - General Mathematics |
| title | Two Non-Congruent Regular Polygons Having Vertices at the Same Distances from the Point |
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