Using conics to construct geometric 3-configurations, part I: symmetrically generalizing the Pappus configuration
Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edg...
Ausführliche Beschreibung
Autor*in: |
Berman, Leah Wrenn [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
2016 |
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Anmerkung: |
© Springer International Publishing 2016 |
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Übergeordnetes Werk: |
Enthalten in: Journal of geometry - Springer International Publishing, 1971, 108(2016), 2 vom: 08. Dez., Seite 591-609 |
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Übergeordnetes Werk: |
volume:108 ; year:2016 ; number:2 ; day:08 ; month:12 ; pages:591-609 |
Links: |
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DOI / URN: |
10.1007/s00022-016-0361-z |
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Katalog-ID: |
OLC2069428672 |
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520 | |a Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edge-labelled $$K_{3,3}$$. This graph quotient, a type of voltage graph, is called the reduced Levi graph of the configuration. In this paper, we generalize this rotational realization of the Pappus configuration by developing a construction technique for a family of geometric configurations with m-fold rotational symmetry for any $$m \ge 3$$ whose reduced Levi graphs are all labelled versions of $$K_{3,3}$$. The constructions use primarily straightedge-and-compass techniques, along with the construction of certain conic sections. | ||
650 | 4 | |a Geometric configuration | |
650 | 4 | |a Pappus configuration | |
650 | 4 | |a Reduced Levi graph | |
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10.1007/s00022-016-0361-z doi (DE-627)OLC2069428672 (DE-He213)s00022-016-0361-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berman, Leah Wrenn verfasserin (orcid)0000-0003-0935-5724 aut Using conics to construct geometric 3-configurations, part I: symmetrically generalizing the Pappus configuration 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edge-labelled $$K_{3,3}$$. This graph quotient, a type of voltage graph, is called the reduced Levi graph of the configuration. In this paper, we generalize this rotational realization of the Pappus configuration by developing a construction technique for a family of geometric configurations with m-fold rotational symmetry for any $$m \ge 3$$ whose reduced Levi graphs are all labelled versions of $$K_{3,3}$$. The constructions use primarily straightedge-and-compass techniques, along with the construction of certain conic sections. Geometric configuration Pappus configuration Reduced Levi graph Enthalten in Journal of geometry Springer International Publishing, 1971 108(2016), 2 vom: 08. Dez., Seite 591-609 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:108 year:2016 number:2 day:08 month:12 pages:591-609 https://doi.org/10.1007/s00022-016-0361-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4277 AR 108 2016 2 08 12 591-609 |
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10.1007/s00022-016-0361-z doi (DE-627)OLC2069428672 (DE-He213)s00022-016-0361-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berman, Leah Wrenn verfasserin (orcid)0000-0003-0935-5724 aut Using conics to construct geometric 3-configurations, part I: symmetrically generalizing the Pappus configuration 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edge-labelled $$K_{3,3}$$. This graph quotient, a type of voltage graph, is called the reduced Levi graph of the configuration. In this paper, we generalize this rotational realization of the Pappus configuration by developing a construction technique for a family of geometric configurations with m-fold rotational symmetry for any $$m \ge 3$$ whose reduced Levi graphs are all labelled versions of $$K_{3,3}$$. The constructions use primarily straightedge-and-compass techniques, along with the construction of certain conic sections. Geometric configuration Pappus configuration Reduced Levi graph Enthalten in Journal of geometry Springer International Publishing, 1971 108(2016), 2 vom: 08. Dez., Seite 591-609 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:108 year:2016 number:2 day:08 month:12 pages:591-609 https://doi.org/10.1007/s00022-016-0361-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4277 AR 108 2016 2 08 12 591-609 |
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10.1007/s00022-016-0361-z doi (DE-627)OLC2069428672 (DE-He213)s00022-016-0361-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berman, Leah Wrenn verfasserin (orcid)0000-0003-0935-5724 aut Using conics to construct geometric 3-configurations, part I: symmetrically generalizing the Pappus configuration 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edge-labelled $$K_{3,3}$$. This graph quotient, a type of voltage graph, is called the reduced Levi graph of the configuration. In this paper, we generalize this rotational realization of the Pappus configuration by developing a construction technique for a family of geometric configurations with m-fold rotational symmetry for any $$m \ge 3$$ whose reduced Levi graphs are all labelled versions of $$K_{3,3}$$. The constructions use primarily straightedge-and-compass techniques, along with the construction of certain conic sections. Geometric configuration Pappus configuration Reduced Levi graph Enthalten in Journal of geometry Springer International Publishing, 1971 108(2016), 2 vom: 08. Dez., Seite 591-609 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:108 year:2016 number:2 day:08 month:12 pages:591-609 https://doi.org/10.1007/s00022-016-0361-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4277 AR 108 2016 2 08 12 591-609 |
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10.1007/s00022-016-0361-z doi (DE-627)OLC2069428672 (DE-He213)s00022-016-0361-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berman, Leah Wrenn verfasserin (orcid)0000-0003-0935-5724 aut Using conics to construct geometric 3-configurations, part I: symmetrically generalizing the Pappus configuration 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edge-labelled $$K_{3,3}$$. This graph quotient, a type of voltage graph, is called the reduced Levi graph of the configuration. In this paper, we generalize this rotational realization of the Pappus configuration by developing a construction technique for a family of geometric configurations with m-fold rotational symmetry for any $$m \ge 3$$ whose reduced Levi graphs are all labelled versions of $$K_{3,3}$$. The constructions use primarily straightedge-and-compass techniques, along with the construction of certain conic sections. Geometric configuration Pappus configuration Reduced Levi graph Enthalten in Journal of geometry Springer International Publishing, 1971 108(2016), 2 vom: 08. Dez., Seite 591-609 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:108 year:2016 number:2 day:08 month:12 pages:591-609 https://doi.org/10.1007/s00022-016-0361-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4277 AR 108 2016 2 08 12 591-609 |
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10.1007/s00022-016-0361-z doi (DE-627)OLC2069428672 (DE-He213)s00022-016-0361-z-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Berman, Leah Wrenn verfasserin (orcid)0000-0003-0935-5724 aut Using conics to construct geometric 3-configurations, part I: symmetrically generalizing the Pappus configuration 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing 2016 Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edge-labelled $$K_{3,3}$$. This graph quotient, a type of voltage graph, is called the reduced Levi graph of the configuration. In this paper, we generalize this rotational realization of the Pappus configuration by developing a construction technique for a family of geometric configurations with m-fold rotational symmetry for any $$m \ge 3$$ whose reduced Levi graphs are all labelled versions of $$K_{3,3}$$. The constructions use primarily straightedge-and-compass techniques, along with the construction of certain conic sections. Geometric configuration Pappus configuration Reduced Levi graph Enthalten in Journal of geometry Springer International Publishing, 1971 108(2016), 2 vom: 08. Dez., Seite 591-609 (DE-627)129288993 (DE-600)120140-2 (DE-576)014470527 0047-2468 nnns volume:108 year:2016 number:2 day:08 month:12 pages:591-609 https://doi.org/10.1007/s00022-016-0361-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4277 AR 108 2016 2 08 12 591-609 |
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Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edge-labelled $$K_{3,3}$$. This graph quotient, a type of voltage graph, is called the reduced Levi graph of the configuration. In this paper, we generalize this rotational realization of the Pappus configuration by developing a construction technique for a family of geometric configurations with m-fold rotational symmetry for any $$m \ge 3$$ whose reduced Levi graphs are all labelled versions of $$K_{3,3}$$. The constructions use primarily straightedge-and-compass techniques, along with the construction of certain conic sections. © Springer International Publishing 2016 |
abstractGer |
Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edge-labelled $$K_{3,3}$$. This graph quotient, a type of voltage graph, is called the reduced Levi graph of the configuration. In this paper, we generalize this rotational realization of the Pappus configuration by developing a construction technique for a family of geometric configurations with m-fold rotational symmetry for any $$m \ge 3$$ whose reduced Levi graphs are all labelled versions of $$K_{3,3}$$. The constructions use primarily straightedge-and-compass techniques, along with the construction of certain conic sections. © Springer International Publishing 2016 |
abstract_unstemmed |
Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edge-labelled $$K_{3,3}$$. This graph quotient, a type of voltage graph, is called the reduced Levi graph of the configuration. In this paper, we generalize this rotational realization of the Pappus configuration by developing a construction technique for a family of geometric configurations with m-fold rotational symmetry for any $$m \ge 3$$ whose reduced Levi graphs are all labelled versions of $$K_{3,3}$$. The constructions use primarily straightedge-and-compass techniques, along with the construction of certain conic sections. © Springer International Publishing 2016 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2069428672</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230323111319.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00022-016-0361-z</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2069428672</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00022-016-0361-z-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Berman, Leah Wrenn</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-0935-5724</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Using conics to construct geometric 3-configurations, part I: symmetrically generalizing the Pappus configuration</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer International Publishing 2016</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The $$(9_{3})$$ Pappus configuration can be realized as a geometric configuration with 3-fold rotational symmetry; using this 3-fold rotation, its Levi graph (the incidence graph for the configuration) can be quotiented by the automorphism corresponding to the 3-fold rotation to form an edge-labelled $$K_{3,3}$$. This graph quotient, a type of voltage graph, is called the reduced Levi graph of the configuration. In this paper, we generalize this rotational realization of the Pappus configuration by developing a construction technique for a family of geometric configurations with m-fold rotational symmetry for any $$m \ge 3$$ whose reduced Levi graphs are all labelled versions of $$K_{3,3}$$. 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