Some Results About Equichordal Convex Bodies
Let K and L be two convex bodies in R n , n ≥ 2 , with L ⊂ int K . We say that L is an equichordal body for K if every chord of K tangent to L has length equal to a given fixed value λ . Barker and Larman (Discrete Math. 241 (1–3), 79–96 (2001)) proved that if L is a ball, then K is a ball concent...
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| Veröffentlicht in: | Discrete & computational geometry 2023-12, Vol.70 (4), p.1741-1750 |
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| container_title | Discrete & computational geometry |
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| creator | Jerónimo-Castro, Jesús Jimenez-Lopez, Francisco G. Morales-Amaya, Efrén |
| description | Let
K
and
L
be two convex bodies in
R
n
,
n
≥
2
, with
L
⊂
int
K
. We say that
L
is an
equichordal body
for
K
if every chord of
K
tangent to
L
has length equal to a given fixed value
λ
. Barker and Larman (Discrete Math.
241
(1–3), 79–96 (2001)) proved that if
L
is a ball, then
K
is a ball concentric with
L
. In this paper we prove that there exist an infinite number of closed curves, different from circles, which possess an equichordal convex body. If the dimension of the space is more than or equal to 3, then only Euclidean balls possess an equichordal convex body. |
| doi_str_mv | 10.1007/s00454-023-00543-8 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2893473036</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2893473036</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-f15765c6c951a5a8332624dfb4a6cd72fecc7af10cd06345f3899323dcdf5bcf3</originalsourceid><addsrcrecordid>eNp9kEtLAzEURoMoWKt_wNWAW6M3uXnMLGupDygIPtYhzUNb2sYmM6L_3tER3Lm6m3O-C4eQUwYXDEBfFgAhBQWOFEAKpPUeGTGBnIIQYp-MgOmGStTqkByVsoKeb6AekfPHtAnVQyjdui3VZJG6tprtuqV7TdnbdTVN2_fwUV0lvwzlmBxEuy7h5PeOyfP17Gl6S-f3N3fTyZw6ZE1LI5NaSadcI5mVtkbkigsfF8Iq5zWPwTltIwPnQaGQEeumQY7e-SgXLuKYnA27bzntulBas0pd3vYvDa8bFBoBVU_xgXI5lZJDNG95ubH50zAw31XMUMX0VcxPFVP3Eg5S6eHtS8h_0_9YX-RiY6Y</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2893473036</pqid></control><display><type>article</type><title>Some Results About Equichordal Convex Bodies</title><source>Springer Nature - Complete Springer Journals</source><creator>Jerónimo-Castro, Jesús ; Jimenez-Lopez, Francisco G. ; Morales-Amaya, Efrén</creator><creatorcontrib>Jerónimo-Castro, Jesús ; Jimenez-Lopez, Francisco G. ; Morales-Amaya, Efrén</creatorcontrib><description>Let
K
and
L
be two convex bodies in
R
n
,
n
≥
2
, with
L
⊂
int
K
. We say that
L
is an
equichordal body
for
K
if every chord of
K
tangent to
L
has length equal to a given fixed value
λ
. Barker and Larman (Discrete Math.
241
(1–3), 79–96 (2001)) proved that if
L
is a ball, then
K
is a ball concentric with
L
. In this paper we prove that there exist an infinite number of closed curves, different from circles, which possess an equichordal convex body. If the dimension of the space is more than or equal to 3, then only Euclidean balls possess an equichordal convex body.</description><identifier>ISSN: 0179-5376</identifier><identifier>EISSN: 1432-0444</identifier><identifier>DOI: 10.1007/s00454-023-00543-8</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Combinatorics ; Computational Mathematics and Numerical Analysis ; Geometry ; Mathematics ; Mathematics and Statistics</subject><ispartof>Discrete & computational geometry, 2023-12, Vol.70 (4), p.1741-1750</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 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><citedby>FETCH-LOGICAL-c319t-f15765c6c951a5a8332624dfb4a6cd72fecc7af10cd06345f3899323dcdf5bcf3</citedby><cites>FETCH-LOGICAL-c319t-f15765c6c951a5a8332624dfb4a6cd72fecc7af10cd06345f3899323dcdf5bcf3</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/s00454-023-00543-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00454-023-00543-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Jerónimo-Castro, Jesús</creatorcontrib><creatorcontrib>Jimenez-Lopez, Francisco G.</creatorcontrib><creatorcontrib>Morales-Amaya, Efrén</creatorcontrib><title>Some Results About Equichordal Convex Bodies</title><title>Discrete & computational geometry</title><addtitle>Discrete Comput Geom</addtitle><description>Let
K
and
L
be two convex bodies in
R
n
,
n
≥
2
, with
L
⊂
int
K
. We say that
L
is an
equichordal body
for
K
if every chord of
K
tangent to
L
has length equal to a given fixed value
λ
. Barker and Larman (Discrete Math.
241
(1–3), 79–96 (2001)) proved that if
L
is a ball, then
K
is a ball concentric with
L
. In this paper we prove that there exist an infinite number of closed curves, different from circles, which possess an equichordal convex body. If the dimension of the space is more than or equal to 3, then only Euclidean balls possess an equichordal convex body.</description><subject>Combinatorics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0179-5376</issn><issn>1432-0444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp9kEtLAzEURoMoWKt_wNWAW6M3uXnMLGupDygIPtYhzUNb2sYmM6L_3tER3Lm6m3O-C4eQUwYXDEBfFgAhBQWOFEAKpPUeGTGBnIIQYp-MgOmGStTqkByVsoKeb6AekfPHtAnVQyjdui3VZJG6tprtuqV7TdnbdTVN2_fwUV0lvwzlmBxEuy7h5PeOyfP17Gl6S-f3N3fTyZw6ZE1LI5NaSadcI5mVtkbkigsfF8Iq5zWPwTltIwPnQaGQEeumQY7e-SgXLuKYnA27bzntulBas0pd3vYvDa8bFBoBVU_xgXI5lZJDNG95ubH50zAw31XMUMX0VcxPFVP3Eg5S6eHtS8h_0_9YX-RiY6Y</recordid><startdate>20231201</startdate><enddate>20231201</enddate><creator>Jerónimo-Castro, Jesús</creator><creator>Jimenez-Lopez, Francisco G.</creator><creator>Morales-Amaya, Efrén</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20231201</creationdate><title>Some Results About Equichordal Convex Bodies</title><author>Jerónimo-Castro, Jesús ; Jimenez-Lopez, Francisco G. ; Morales-Amaya, Efrén</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-f15765c6c951a5a8332624dfb4a6cd72fecc7af10cd06345f3899323dcdf5bcf3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Combinatorics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jerónimo-Castro, Jesús</creatorcontrib><creatorcontrib>Jimenez-Lopez, Francisco G.</creatorcontrib><creatorcontrib>Morales-Amaya, Efrén</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer science database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>ProQuest_Research Library</collection><collection>ProQuest Science Journals</collection><collection>ProQuest Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>ProQuest advanced technologies & aerospace journals</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Research Library China</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering collection</collection><collection>ProQuest Central Basic</collection><jtitle>Discrete & computational geometry</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>Morales-Amaya, Efrén</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some Results About Equichordal Convex Bodies</atitle><jtitle>Discrete & computational geometry</jtitle><stitle>Discrete Comput Geom</stitle><date>2023-12-01</date><risdate>2023</risdate><volume>70</volume><issue>4</issue><spage>1741</spage><epage>1750</epage><pages>1741-1750</pages><issn>0179-5376</issn><eissn>1432-0444</eissn><abstract>Let
K
and
L
be two convex bodies in
R
n
,
n
≥
2
, with
L
⊂
int
K
. We say that
L
is an
equichordal body
for
K
if every chord of
K
tangent to
L
has length equal to a given fixed value
λ
. Barker and Larman (Discrete Math.
241
(1–3), 79–96 (2001)) proved that if
L
is a ball, then
K
is a ball concentric with
L
. In this paper we prove that there exist an infinite number of closed curves, different from circles, which possess an equichordal convex body. If the dimension of the space is more than or equal to 3, then only Euclidean balls possess an equichordal convex body.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00454-023-00543-8</doi><tpages>10</tpages></addata></record> |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Combinatorics Computational Mathematics and Numerical Analysis Geometry Mathematics Mathematics and Statistics |
| title | Some Results About Equichordal Convex Bodies |
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