Some characterizations of the circle related to circumscribed equiangular polygons

Some characterizations of the circle related to circumscribed equiangular polygons

The main purpose of this note is to prove the following: let n ≥ 3 be a fixed integer number and let K be a convex body such that for every equiangular circumscribed n -gon, the midpoints of its sides belong to K . Then K is a disc. We also prove that a 3-dimensional convex body K such that the cent...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Boletín de la Sociedad Matemática Mexicana 2021-11, Vol.27 (3), Article 67
Hauptverfasser: Jerónimo-Castro, Jesús, Jimenez-Lopez, Francisco G., Velasco-García, Ulises
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Original Article
Tetrahedra
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue 3
container_start_page
container_title Boletín de la Sociedad Matemática Mexicana
container_volume 27
creator Jerónimo-Castro, Jesús
Jimenez-Lopez, Francisco G.
Velasco-García, Ulises
description The main purpose of this note is to prove the following: let n ≥ 3 be a fixed integer number and let K be a convex body such that for every equiangular circumscribed n -gon, the midpoints of its sides belong to K . Then K is a disc. We also prove that a 3-dimensional convex body K such that the centers of the faces of all its circumscribed regular tetrahedra belong to K is a ball.
doi_str_mv 10.1007/s40590-021-00372-w
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2564151186</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2564151186</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-508ced642ec0414770c0c5a1e397d096e14b303cea62cfa8c3364d4a8e2a60743</originalsourceid><addsrcrecordid>eNp9kE1Lw0AQhhdRsNT-AU8Bz6uzn0mOUvwCQfADvC3bzaRNSbPtbkKpv961Ebx5GnjneWbgJeSSwTUDyG-iBFUCBc4ogMg53Z-QCeelplKW6pRMWAIoZ-LznMxiXAMAYwIUqAl5ffMbzNzKBut6DM2X7RvfxczXWb9Kiya4FrOAre2xynp_TIZNdKFZpAB3Q2O75dDakG19e1gm94Kc1baNOPudU_Jxf_c-f6TPLw9P89tn6gQre6qgcFhpydGBZDLPwYFTlqEo8wpKjUwuBAiHVnNX28IJoWUlbYHcasilmJKr8e42-N2AsTdrP4QuvTRcackUY4VOFB8pF3yMAWuzDc3GhoNhYH7qM2N9JtVnjvWZfZLEKMUEd0sMf6f_sb4BRwlznw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2564151186</pqid></control><display><type>article</type><title>Some characterizations of the circle related to circumscribed equiangular polygons</title><source>SpringerLink Journals - AutoHoldings</source><creator>Jerónimo-Castro, Jesús ; Jimenez-Lopez, Francisco G. ; Velasco-García, Ulises</creator><creatorcontrib>Jerónimo-Castro, Jesús ; Jimenez-Lopez, Francisco G. ; Velasco-García, Ulises</creatorcontrib><description>The main purpose of this note is to prove the following: let n ≥ 3 be a fixed integer number and let K be a convex body such that for every equiangular circumscribed n -gon, the midpoints of its sides belong to K . Then K is a disc. We also prove that a 3-dimensional convex body K such that the centers of the faces of all its circumscribed regular tetrahedra belong to K is a ball.</description><identifier>ISSN: 1405-213X</identifier><identifier>EISSN: 2296-4495</identifier><identifier>DOI: 10.1007/s40590-021-00372-w</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematics ; Mathematics and Statistics ; Original Article ; Tetrahedra</subject><ispartof>Boletín de la Sociedad Matemática Mexicana, 2021-11, Vol.27 (3), Article 67</ispartof><rights>Sociedad Matemática Mexicana 2021</rights><rights>Sociedad Matemática Mexicana 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-508ced642ec0414770c0c5a1e397d096e14b303cea62cfa8c3364d4a8e2a60743</citedby><cites>FETCH-LOGICAL-c319t-508ced642ec0414770c0c5a1e397d096e14b303cea62cfa8c3364d4a8e2a60743</cites><orcidid>0000-0002-2630-9095</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40590-021-00372-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40590-021-00372-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Jerónimo-Castro, Jesús</creatorcontrib><creatorcontrib>Jimenez-Lopez, Francisco G.</creatorcontrib><creatorcontrib>Velasco-García, Ulises</creatorcontrib><title>Some characterizations of the circle related to circumscribed equiangular polygons</title><title>Boletín de la Sociedad Matemática Mexicana</title><addtitle>Bol. Soc. Mat. Mex</addtitle><description>The main purpose of this note is to prove the following: let n ≥ 3 be a fixed integer number and let K be a convex body such that for every equiangular circumscribed n -gon, the midpoints of its sides belong to K . Then K is a disc. We also prove that a 3-dimensional convex body K such that the centers of the faces of all its circumscribed regular tetrahedra belong to K is a ball.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Article</subject><subject>Tetrahedra</subject><issn>1405-213X</issn><issn>2296-4495</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE1Lw0AQhhdRsNT-AU8Bz6uzn0mOUvwCQfADvC3bzaRNSbPtbkKpv961Ebx5GnjneWbgJeSSwTUDyG-iBFUCBc4ogMg53Z-QCeelplKW6pRMWAIoZ-LznMxiXAMAYwIUqAl5ffMbzNzKBut6DM2X7RvfxczXWb9Kiya4FrOAre2xynp_TIZNdKFZpAB3Q2O75dDakG19e1gm94Kc1baNOPudU_Jxf_c-f6TPLw9P89tn6gQre6qgcFhpydGBZDLPwYFTlqEo8wpKjUwuBAiHVnNX28IJoWUlbYHcasilmJKr8e42-N2AsTdrP4QuvTRcackUY4VOFB8pF3yMAWuzDc3GhoNhYH7qM2N9JtVnjvWZfZLEKMUEd0sMf6f_sb4BRwlznw</recordid><startdate>20211101</startdate><enddate>20211101</enddate><creator>Jerónimo-Castro, Jesús</creator><creator>Jimenez-Lopez, Francisco G.</creator><creator>Velasco-García, Ulises</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-2630-9095</orcidid></search><sort><creationdate>20211101</creationdate><title>Some characterizations of the circle related to circumscribed equiangular polygons</title><author>Jerónimo-Castro, Jesús ; Jimenez-Lopez, Francisco G. ; Velasco-García, Ulises</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-508ced642ec0414770c0c5a1e397d096e14b303cea62cfa8c3364d4a8e2a60743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Article</topic><topic>Tetrahedra</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jerónimo-Castro, Jesús</creatorcontrib><creatorcontrib>Jimenez-Lopez, Francisco G.</creatorcontrib><creatorcontrib>Velasco-García, Ulises</creatorcontrib><collection>CrossRef</collection><jtitle>Boletín de la Sociedad Matemática Mexicana</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jerónimo-Castro, Jesús</au><au>Jimenez-Lopez, Francisco G.</au><au>Velasco-García, Ulises</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some characterizations of the circle related to circumscribed equiangular polygons</atitle><jtitle>Boletín de la Sociedad Matemática Mexicana</jtitle><stitle>Bol. Soc. Mat. Mex</stitle><date>2021-11-01</date><risdate>2021</risdate><volume>27</volume><issue>3</issue><artnum>67</artnum><issn>1405-213X</issn><eissn>2296-4495</eissn><abstract>The main purpose of this note is to prove the following: let n ≥ 3 be a fixed integer number and let K be a convex body such that for every equiangular circumscribed n -gon, the midpoints of its sides belong to K . Then K is a disc. We also prove that a 3-dimensional convex body K such that the centers of the faces of all its circumscribed regular tetrahedra belong to K is a ball.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40590-021-00372-w</doi><orcidid>https://orcid.org/0000-0002-2630-9095</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 1405-213X
ispartof Boletín de la Sociedad Matemática Mexicana, 2021-11, Vol.27 (3), Article 67
issn 1405-213X
2296-4495
language eng
recordid cdi_proquest_journals_2564151186
source SpringerLink Journals - AutoHoldings
subjects Mathematics
Mathematics and Statistics
Original Article
Tetrahedra
title Some characterizations of the circle related to circumscribed equiangular polygons
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T18%3A40%3A52IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Some%20characterizations%20of%20the%20circle%20related%20to%20circumscribed%20equiangular%20polygons&rft.jtitle=Bolet%C3%ADn%20de%20la%20Sociedad%20Matem%C3%A1tica%20Mexicana&rft.au=Jer%C3%B3nimo-Castro,%20Jes%C3%BAs&rft.date=2021-11-01&rft.volume=27&rft.issue=3&rft.artnum=67&rft.issn=1405-213X&rft.eissn=2296-4495&rft_id=info:doi/10.1007/s40590-021-00372-w&rft_dat=%3Cproquest_cross%3E2564151186%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2564151186&rft_id=info:pmid/&rfr_iscdi=true