The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space

A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surf...
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Autor*in:	Serkan Çelik [verfasserIn] Hacı Bayram Karadağ [verfasserIn] Hatice Kuşak Samancı [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	conchoidal curve twisted surfaces involute curve Bertrand curve anti-symmetric rotation matrix

Übergeordnetes Werk:	In: Symmetry - MDPI AG, 2009, 15(2023), 6, p 1191
Übergeordnetes Werk:	volume:15 ; year:2023 ; number:6, p 1191

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/sym15061191

Katalog-ID:	DOAJ094050724

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allfields	10.3390/sym15061191 doi (DE-627)DOAJ094050724 (DE-599)DOAJc89c696f50a44a4c8b08e9d1fc80c048 DE-627 ger DE-627 rakwb eng QA1-939 Serkan Çelik verfasserin aut The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature. conchoidal curve twisted surfaces involute curve Bertrand curve anti-symmetric rotation matrix Mathematics Hacı Bayram Karadağ verfasserin aut Hatice Kuşak Samancı verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 6, p 1191 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:6, p 1191 https://doi.org/10.3390/sym15061191 kostenfrei https://doaj.org/article/c89c696f50a44a4c8b08e9d1fc80c048 kostenfrei https://www.mdpi.com/2073-8994/15/6/1191 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 6, p 1191
spelling	10.3390/sym15061191 doi (DE-627)DOAJ094050724 (DE-599)DOAJc89c696f50a44a4c8b08e9d1fc80c048 DE-627 ger DE-627 rakwb eng QA1-939 Serkan Çelik verfasserin aut The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature. conchoidal curve twisted surfaces involute curve Bertrand curve anti-symmetric rotation matrix Mathematics Hacı Bayram Karadağ verfasserin aut Hatice Kuşak Samancı verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 6, p 1191 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:6, p 1191 https://doi.org/10.3390/sym15061191 kostenfrei https://doaj.org/article/c89c696f50a44a4c8b08e9d1fc80c048 kostenfrei https://www.mdpi.com/2073-8994/15/6/1191 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 6, p 1191
allfields_unstemmed	10.3390/sym15061191 doi (DE-627)DOAJ094050724 (DE-599)DOAJc89c696f50a44a4c8b08e9d1fc80c048 DE-627 ger DE-627 rakwb eng QA1-939 Serkan Çelik verfasserin aut The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature. conchoidal curve twisted surfaces involute curve Bertrand curve anti-symmetric rotation matrix Mathematics Hacı Bayram Karadağ verfasserin aut Hatice Kuşak Samancı verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 6, p 1191 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:6, p 1191 https://doi.org/10.3390/sym15061191 kostenfrei https://doaj.org/article/c89c696f50a44a4c8b08e9d1fc80c048 kostenfrei https://www.mdpi.com/2073-8994/15/6/1191 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 6, p 1191
allfieldsGer	10.3390/sym15061191 doi (DE-627)DOAJ094050724 (DE-599)DOAJc89c696f50a44a4c8b08e9d1fc80c048 DE-627 ger DE-627 rakwb eng QA1-939 Serkan Çelik verfasserin aut The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature. conchoidal curve twisted surfaces involute curve Bertrand curve anti-symmetric rotation matrix Mathematics Hacı Bayram Karadağ verfasserin aut Hatice Kuşak Samancı verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 6, p 1191 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:6, p 1191 https://doi.org/10.3390/sym15061191 kostenfrei https://doaj.org/article/c89c696f50a44a4c8b08e9d1fc80c048 kostenfrei https://www.mdpi.com/2073-8994/15/6/1191 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 6, p 1191
allfieldsSound	10.3390/sym15061191 doi (DE-627)DOAJ094050724 (DE-599)DOAJc89c696f50a44a4c8b08e9d1fc80c048 DE-627 ger DE-627 rakwb eng QA1-939 Serkan Çelik verfasserin aut The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature. conchoidal curve twisted surfaces involute curve Bertrand curve anti-symmetric rotation matrix Mathematics Hacı Bayram Karadağ verfasserin aut Hatice Kuşak Samancı verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 6, p 1191 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:6, p 1191 https://doi.org/10.3390/sym15061191 kostenfrei https://doaj.org/article/c89c696f50a44a4c8b08e9d1fc80c048 kostenfrei https://www.mdpi.com/2073-8994/15/6/1191 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 6, p 1191
language	English
source	In Symmetry 15(2023), 6, p 1191 volume:15 year:2023 number:6, p 1191
sourceStr	In Symmetry 15(2023), 6, p 1191 volume:15 year:2023 number:6, p 1191
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	conchoidal curve twisted surfaces involute curve Bertrand curve anti-symmetric rotation matrix Mathematics
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container_title	Symmetry
authorswithroles_txt_mv	Serkan Çelik @@aut@@ Hacı Bayram Karadağ @@aut@@ Hatice Kuşak Samancı @@aut@@
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callnumber-first	Q - Science
author	Serkan Çelik
spellingShingle	Serkan Çelik misc QA1-939 misc conchoidal curve misc twisted surfaces misc involute curve misc Bertrand curve misc anti-symmetric rotation matrix misc Mathematics The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space
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topic_title	QA1-939 The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space conchoidal curve twisted surfaces involute curve Bertrand curve anti-symmetric rotation matrix
topic	misc QA1-939 misc conchoidal curve misc twisted surfaces misc involute curve misc Bertrand curve misc anti-symmetric rotation matrix misc Mathematics
topic_unstemmed	misc QA1-939 misc conchoidal curve misc twisted surfaces misc involute curve misc Bertrand curve misc anti-symmetric rotation matrix misc Mathematics
topic_browse	misc QA1-939 misc conchoidal curve misc twisted surfaces misc involute curve misc Bertrand curve misc anti-symmetric rotation matrix misc Mathematics
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title	The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space
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title_auth	The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space
abstract	A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature.
abstractGer	A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature.
abstract_unstemmed	A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature.
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title_short	The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space
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The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space

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