Some characterizations of the disc by properties of isoptic triangles
The main result in this article is the following: Let K ⊂ R 2 be a regular convex body and let α , β , θ , be three angles such that K has α -chords, β -chords, and θ -chords of constant length and α + β + θ = π , then K is a disc. We also prove another characterization of the disc with respect to p...
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| Veröffentlicht in: | Aequationes mathematicae 2024-04, Vol.98 (2), p.591-602 |
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| container_title | Aequationes mathematicae |
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| creator | Ayala-Figueroa, Rafael I. González-García, Iván Jerónimo-Castro, Jesús Jimenez-Lopez, Francisco G. |
| description | The main result in this article is the following: Let
K
⊂
R
2
be a regular convex body and let
α
,
β
,
θ
, be three angles such that
K
has
α
-chords,
β
-chords, and
θ
-chords of constant length and
α
+
β
+
θ
=
π
, then
K
is a disc. We also prove another characterization of the disc with respect to properties of its
(
α
,
β
,
θ
)
-circumscribed triangles. |
| doi_str_mv | 10.1007/s00010-023-00983-w |
| format | Article |
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K
⊂
R
2
be a regular convex body and let
α
,
β
,
θ
, be three angles such that
K
has
α
-chords,
β
-chords, and
θ
-chords of constant length and
α
+
β
+
θ
=
π
, then
K
is a disc. We also prove another characterization of the disc with respect to properties of its
(
α
,
β
,
θ
)
-circumscribed triangles.</description><identifier>ISSN: 0001-9054</identifier><identifier>EISSN: 1420-8903</identifier><identifier>DOI: 10.1007/s00010-023-00983-w</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Combinatorics ; Mathematics ; Mathematics and Statistics ; Triangles</subject><ispartof>Aequationes mathematicae, 2024-04, Vol.98 (2), p.591-602</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-7299cf55da9ed136be3dbb7e2851c11ed5ab5d1080e54ad8d1d309c45f1184ef3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00010-023-00983-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00010-023-00983-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Ayala-Figueroa, Rafael I.</creatorcontrib><creatorcontrib>González-García, Iván</creatorcontrib><creatorcontrib>Jerónimo-Castro, Jesús</creatorcontrib><creatorcontrib>Jimenez-Lopez, Francisco G.</creatorcontrib><title>Some characterizations of the disc by properties of isoptic triangles</title><title>Aequationes mathematicae</title><addtitle>Aequat. Math</addtitle><description>The main result in this article is the following: Let
K
⊂
R
2
be a regular convex body and let
α
,
β
,
θ
, be three angles such that
K
has
α
-chords,
β
-chords, and
θ
-chords of constant length and
α
+
β
+
θ
=
π
, then
K
is a disc. We also prove another characterization of the disc with respect to properties of its
(
α
,
β
,
θ
)
-circumscribed triangles.</description><subject>Analysis</subject><subject>Combinatorics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Triangles</subject><issn>0001-9054</issn><issn>1420-8903</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKt_wNOC5-hMsunuHqXUDyh4UM8hm8y2KW13TVJK_fVuu4I3T8PwfszwMHaLcI8AxUMEAAQOQnKAqpR8f8ZGmAvgZQXynI2OOq9A5ZfsKsZVv4mikCM2e283lNmlCcYmCv7bJN9uY9Y2WVpS5ny0WX3IutB2FJKnk-Jj2yVvsxS82S7WFK_ZRWPWkW5-55h9Ps0-pi98_vb8On2ccysKSLwQVWUbpZypyKGc1CRdXRckSoUWkZwytXIIJZDKjSsdOgmVzVWDWObUyDG7G3r7f752FJNetbuw7U9qCajyXEwk9i4xuGxoYwzU6C74jQkHjaCPuPSAS_e49AmX3vchOYRib94uKPxV_5P6AVRDbjY</recordid><startdate>20240401</startdate><enddate>20240401</enddate><creator>Ayala-Figueroa, Rafael I.</creator><creator>González-García, Iván</creator><creator>Jerónimo-Castro, Jesús</creator><creator>Jimenez-Lopez, Francisco G.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20240401</creationdate><title>Some characterizations of the disc by properties of isoptic triangles</title><author>Ayala-Figueroa, Rafael I. ; González-García, Iván ; Jerónimo-Castro, Jesús ; Jimenez-Lopez, Francisco G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-7299cf55da9ed136be3dbb7e2851c11ed5ab5d1080e54ad8d1d309c45f1184ef3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Analysis</topic><topic>Combinatorics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Triangles</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ayala-Figueroa, Rafael I.</creatorcontrib><creatorcontrib>González-García, Iván</creatorcontrib><creatorcontrib>Jerónimo-Castro, Jesús</creatorcontrib><creatorcontrib>Jimenez-Lopez, Francisco G.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Aequationes mathematicae</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ayala-Figueroa, Rafael I.</au><au>González-García, Iván</au><au>Jerónimo-Castro, Jesús</au><au>Jimenez-Lopez, Francisco G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some characterizations of the disc by properties of isoptic triangles</atitle><jtitle>Aequationes mathematicae</jtitle><stitle>Aequat. Math</stitle><date>2024-04-01</date><risdate>2024</risdate><volume>98</volume><issue>2</issue><spage>591</spage><epage>602</epage><pages>591-602</pages><issn>0001-9054</issn><eissn>1420-8903</eissn><abstract>The main result in this article is the following: Let
K
⊂
R
2
be a regular convex body and let
α
,
β
,
θ
, be three angles such that
K
has
α
-chords,
β
-chords, and
θ
-chords of constant length and
α
+
β
+
θ
=
π
, then
K
is a disc. We also prove another characterization of the disc with respect to properties of its
(
α
,
β
,
θ
)
-circumscribed triangles.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00010-023-00983-w</doi><tpages>12</tpages></addata></record> |
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| language | eng |
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| subjects | Analysis Combinatorics Mathematics Mathematics and Statistics Triangles |
| title | Some characterizations of the disc by properties of isoptic triangles |
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