Some Results About Equichordal Convex Bodies

Abstract Let K and L be two convex bodies in %${\mathbb {R}}^n%$, %$n\ge 2%$, with %$L\subset {{\,\textrm{int}\,}}K%$. 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 %$\lambda %$. Barker and Larman (Discrete Math. 241(1–3), 79–96 (...
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Autor*in:	Jerónimo-Castro, Jesús [verfasserIn] Jimenez-Lopez, Francisco G. Morales-Amaya, Efrén

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Euclidean sphere Equichordal body Isoptic curves

Anmerkung:	© 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.

Übergeordnetes Werk:	Enthalten in: Discrete & computational geometry - New York, NY : Springer, 1986, 70(2023), 4 vom: 28. Juli, Seite 1741-1750
Übergeordnetes Werk:	volume:70 ; year:2023 ; number:4 ; day:28 ; month:07 ; pages:1741-1750

Links:	Volltext

DOI / URN:	10.1007/s00454-023-00543-8

Katalog-ID:	SPR053857526

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allfields	10.1007/s00454-023-00543-8 doi (DE-627)SPR053857526 (SPR)s00454-023-00543-8-e DE-627 ger DE-627 rakwb eng Jerónimo-Castro, Jesús verfasserin aut Some Results About Equichordal Convex Bodies 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © 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. Abstract Let K and L be two convex bodies in %${\mathbb {R}}^n%$, %$n\ge 2%$, with %$L\subset {{\,\textrm{int}\,}}K%$. 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 %$\lambda %$. 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. Euclidean sphere (dpeaa)DE-He213 Equichordal body (dpeaa)DE-He213 Isoptic curves (dpeaa)DE-He213 Jimenez-Lopez, Francisco G. aut Morales-Amaya, Efrén aut Enthalten in Discrete & computational geometry New York, NY : Springer, 1986 70(2023), 4 vom: 28. Juli, Seite 1741-1750 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:70 year:2023 number:4 day:28 month:07 pages:1741-1750 https://dx.doi.org/10.1007/s00454-023-00543-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 70 2023 4 28 07 1741-1750
spelling	10.1007/s00454-023-00543-8 doi (DE-627)SPR053857526 (SPR)s00454-023-00543-8-e DE-627 ger DE-627 rakwb eng Jerónimo-Castro, Jesús verfasserin aut Some Results About Equichordal Convex Bodies 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © 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. Abstract Let K and L be two convex bodies in %${\mathbb {R}}^n%$, %$n\ge 2%$, with %$L\subset {{\,\textrm{int}\,}}K%$. 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 %$\lambda %$. 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. Euclidean sphere (dpeaa)DE-He213 Equichordal body (dpeaa)DE-He213 Isoptic curves (dpeaa)DE-He213 Jimenez-Lopez, Francisco G. aut Morales-Amaya, Efrén aut Enthalten in Discrete & computational geometry New York, NY : Springer, 1986 70(2023), 4 vom: 28. Juli, Seite 1741-1750 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:70 year:2023 number:4 day:28 month:07 pages:1741-1750 https://dx.doi.org/10.1007/s00454-023-00543-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 70 2023 4 28 07 1741-1750
allfields_unstemmed	10.1007/s00454-023-00543-8 doi (DE-627)SPR053857526 (SPR)s00454-023-00543-8-e DE-627 ger DE-627 rakwb eng Jerónimo-Castro, Jesús verfasserin aut Some Results About Equichordal Convex Bodies 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © 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. Abstract Let K and L be two convex bodies in %${\mathbb {R}}^n%$, %$n\ge 2%$, with %$L\subset {{\,\textrm{int}\,}}K%$. 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 %$\lambda %$. 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. Euclidean sphere (dpeaa)DE-He213 Equichordal body (dpeaa)DE-He213 Isoptic curves (dpeaa)DE-He213 Jimenez-Lopez, Francisco G. aut Morales-Amaya, Efrén aut Enthalten in Discrete & computational geometry New York, NY : Springer, 1986 70(2023), 4 vom: 28. Juli, Seite 1741-1750 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:70 year:2023 number:4 day:28 month:07 pages:1741-1750 https://dx.doi.org/10.1007/s00454-023-00543-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 70 2023 4 28 07 1741-1750
allfieldsGer	10.1007/s00454-023-00543-8 doi (DE-627)SPR053857526 (SPR)s00454-023-00543-8-e DE-627 ger DE-627 rakwb eng Jerónimo-Castro, Jesús verfasserin aut Some Results About Equichordal Convex Bodies 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © 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. Abstract Let K and L be two convex bodies in %${\mathbb {R}}^n%$, %$n\ge 2%$, with %$L\subset {{\,\textrm{int}\,}}K%$. 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 %$\lambda %$. 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. Euclidean sphere (dpeaa)DE-He213 Equichordal body (dpeaa)DE-He213 Isoptic curves (dpeaa)DE-He213 Jimenez-Lopez, Francisco G. aut Morales-Amaya, Efrén aut Enthalten in Discrete & computational geometry New York, NY : Springer, 1986 70(2023), 4 vom: 28. Juli, Seite 1741-1750 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:70 year:2023 number:4 day:28 month:07 pages:1741-1750 https://dx.doi.org/10.1007/s00454-023-00543-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 70 2023 4 28 07 1741-1750
allfieldsSound	10.1007/s00454-023-00543-8 doi (DE-627)SPR053857526 (SPR)s00454-023-00543-8-e DE-627 ger DE-627 rakwb eng Jerónimo-Castro, Jesús verfasserin aut Some Results About Equichordal Convex Bodies 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © 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. Abstract Let K and L be two convex bodies in %${\mathbb {R}}^n%$, %$n\ge 2%$, with %$L\subset {{\,\textrm{int}\,}}K%$. 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 %$\lambda %$. 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. Euclidean sphere (dpeaa)DE-He213 Equichordal body (dpeaa)DE-He213 Isoptic curves (dpeaa)DE-He213 Jimenez-Lopez, Francisco G. aut Morales-Amaya, Efrén aut Enthalten in Discrete & computational geometry New York, NY : Springer, 1986 70(2023), 4 vom: 28. Juli, Seite 1741-1750 (DE-627)253722330 (DE-600)1459007-4 1432-0444 nnns volume:70 year:2023 number:4 day:28 month:07 pages:1741-1750 https://dx.doi.org/10.1007/s00454-023-00543-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 70 2023 4 28 07 1741-1750
language	English
source	Enthalten in Discrete & computational geometry 70(2023), 4 vom: 28. Juli, Seite 1741-1750 volume:70 year:2023 number:4 day:28 month:07 pages:1741-1750
sourceStr	Enthalten in Discrete & computational geometry 70(2023), 4 vom: 28. Juli, Seite 1741-1750 volume:70 year:2023 number:4 day:28 month:07 pages:1741-1750
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Euclidean sphere Equichordal body Isoptic curves
isfreeaccess_bool	false
container_title	Discrete & computational geometry
authorswithroles_txt_mv	Jerónimo-Castro, Jesús @@aut@@ Jimenez-Lopez, Francisco G. @@aut@@ Morales-Amaya, Efrén @@aut@@
publishDateDaySort_date	2023-07-28T00:00:00Z
hierarchy_top_id	253722330
id	SPR053857526
language_de	englisch
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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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let K and L be two convex bodies in %${\mathbb {R}}^n%$, %$n\ge 2%$, with %$L\subset {{\,\textrm{int}\,}}K%$. 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 %$\lambda %$. 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. 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author	Jerónimo-Castro, Jesús
spellingShingle	Jerónimo-Castro, Jesús misc Euclidean sphere misc Equichordal body misc Isoptic curves Some Results About Equichordal Convex Bodies
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topic_title	Some Results About Equichordal Convex Bodies Euclidean sphere (dpeaa)DE-He213 Equichordal body (dpeaa)DE-He213 Isoptic curves (dpeaa)DE-He213
topic	misc Euclidean sphere misc Equichordal body misc Isoptic curves
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title	Some Results About Equichordal Convex Bodies
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title_full	Some Results About Equichordal Convex Bodies
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title_sort	some results about equichordal convex bodies
title_auth	Some Results About Equichordal Convex Bodies
abstract	Abstract Let K and L be two convex bodies in %${\mathbb {R}}^n%$, %$n\ge 2%$, with %$L\subset {{\,\textrm{int}\,}}K%$. 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 %$\lambda %$. 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. © 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.
abstractGer	Abstract Let K and L be two convex bodies in %${\mathbb {R}}^n%$, %$n\ge 2%$, with %$L\subset {{\,\textrm{int}\,}}K%$. 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 %$\lambda %$. 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. © 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.
abstract_unstemmed	Abstract Let K and L be two convex bodies in %${\mathbb {R}}^n%$, %$n\ge 2%$, with %$L\subset {{\,\textrm{int}\,}}K%$. 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 %$\lambda %$. 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. © 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.
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container_issue	4
title_short	Some Results About Equichordal Convex Bodies
url	https://dx.doi.org/10.1007/s00454-023-00543-8
remote_bool	true
author2	Jimenez-Lopez, Francisco G. Morales-Amaya, Efrén
author2Str	Jimenez-Lopez, Francisco G. Morales-Amaya, Efrén
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doi_str	10.1007/s00454-023-00543-8
up_date	2024-07-03T22:30:35.274Z
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