The Number of Configurations of Radii that Can Occur in Compact Packings of the Plane with Discs of n Sizes is Finite.
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| Title: | The Number of Configurations of Radii that Can Occur in Compact Packings of the Plane with Discs of n Sizes is Finite. |
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| Authors: | Messerschmidt, Miek1 (AUTHOR) miek.messerschmidt@up.ac.za |
| Source: | Discrete & Computational Geometry. Mar2024, Vol. 71 Issue 2, p667-682. 16p. |
| Subjects: | Compact discs |
| Abstract: | By a compact packing of the plane by discs, P, we mean a collection of closed discs in the plane with pairwise disjoint interior so that, for every disc C ∈ P , there exists a sequence of discs D 0 , ... , D m - 1 ∈ P so that each D i is tangent to both C and D i + 1 m o d m . We prove, for every n ∈ N , that there exist only finitely many tuples (r 0 , r 1 , ... , r n - 1) ∈ R n with 0 < r 0 < r 1 < ... < r n - 1 = 1 that can occur as the radii of the discs in any compact packing of the plane with n distinct sizes of disc. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 175234585 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Number of Configurations of Radii that Can Occur in Compact Packings of the Plane with Discs of n Sizes is Finite. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Messerschmidt%2C+Miek%22">Messerschmidt, Miek</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> miek.messerschmidt@up.ac.za</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+%26+Computational+Geometry%22">Discrete & Computational Geometry</searchLink>. Mar2024, Vol. 71 Issue 2, p667-682. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Compact+discs%22">Compact discs</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: By a compact packing of the plane by discs, P, we mean a collection of closed discs in the plane with pairwise disjoint interior so that, for every disc C ∈ P , there exists a sequence of discs D 0 , ... , D m - 1 ∈ P so that each D i is tangent to both C and D i + 1 m o d m . We prove, for every n ∈ N , that there exist only finitely many tuples (r 0 , r 1 , ... , r n - 1) ∈ R n with 0 < r 0 < r 1 < ... < r n - 1 = 1 that can occur as the radii of the discs in any compact packing of the plane with n distinct sizes of disc. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=175234585 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00454-022-00471-z Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 667 Subjects: – SubjectFull: Compact discs Type: general Titles: – TitleFull: The Number of Configurations of Radii that Can Occur in Compact Packings of the Plane with Discs of n Sizes is Finite. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Messerschmidt, Miek IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 01795376 Numbering: – Type: volume Value: 71 – Type: issue Value: 2 Titles: – TitleFull: Discrete & Computational Geometry Type: main |
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