R-hulloid of the vertices of a tetrahedron.
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| Title: | R-hulloid of the vertices of a tetrahedron. |
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| Authors: | Longinetti, Marco1 (AUTHOR), Naldi, Simone1,2 (AUTHOR) simone.naldi@unilim.fr, Venturi, Adriana3 (AUTHOR) |
| Source: | Advances in Applied Mathematics. May2026, Vol. 176, pN.PAG-N.PAG. 1p. |
| Subjects: | Tetrahedra, Euclidean geometry, Johnson, Samuel, 1709-1784, Spherical geometry, Solid geometry |
| Abstract: | The R -hulloid, in the Euclidean space R 3 , of the set of vertices V of a tetrahedron T is the minimal closed set containing V such that its complement is the union of open balls of radius R. When R is greater than the circumradius of T , the boundary of the R -hulloid consists of V and possibly of four spherical subsets of well defined spheres of radius R through the vertices of T. The existence of a value R ⁎ such that these subsets collapse into a point O ⁎ , in the interior of T , is investigated; in such a case O ⁎ belongs to four spheres of radius R ⁎ , each one through three vertices of T and not containing the fourth one. As a consequence, the range of ρ such that V is a ρ -body is described completely. This work generalizes to dimension three previous results, proved in the planar case and related to the three circles Johnson's Theorem. [ABSTRACT FROM AUTHOR] |
| Copyright of Advances in Applied Mathematics is the property of Academic Press Inc. 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 | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192004316 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: R-hulloid of the vertices of a tetrahedron. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Longinetti%2C+Marco%22">Longinetti, Marco</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Naldi%2C+Simone%22">Naldi, Simone</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> simone.naldi@unilim.fr</i><br /><searchLink fieldCode="AR" term="%22Venturi%2C+Adriana%22">Venturi, Adriana</searchLink><relatesTo>3</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Advances+in+Applied+Mathematics%22">Advances in Applied Mathematics</searchLink>. May2026, Vol. 176, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Tetrahedra%22">Tetrahedra</searchLink><br /><searchLink fieldCode="DE" term="%22Euclidean+geometry%22">Euclidean geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Johnson%2C+Samuel%2C+1709-1784%22">Johnson, Samuel, 1709-1784</searchLink><br /><searchLink fieldCode="DE" term="%22Spherical+geometry%22">Spherical geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Solid+geometry%22">Solid geometry</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The R -hulloid, in the Euclidean space R 3 , of the set of vertices V of a tetrahedron T is the minimal closed set containing V such that its complement is the union of open balls of radius R. When R is greater than the circumradius of T , the boundary of the R -hulloid consists of V and possibly of four spherical subsets of well defined spheres of radius R through the vertices of T. The existence of a value R ⁎ such that these subsets collapse into a point O ⁎ , in the interior of T , is investigated; in such a case O ⁎ belongs to four spheres of radius R ⁎ , each one through three vertices of T and not containing the fourth one. As a consequence, the range of ρ such that V is a ρ -body is described completely. This work generalizes to dimension three previous results, proved in the planar case and related to the three circles Johnson's Theorem. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Advances in Applied Mathematics is the property of Academic Press Inc. 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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.aam.2026.103056 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Tetrahedra Type: general – SubjectFull: Euclidean geometry Type: general – SubjectFull: Johnson, Samuel, 1709-1784 Type: general – SubjectFull: Spherical geometry Type: general – SubjectFull: Solid geometry Type: general Titles: – TitleFull: R-hulloid of the vertices of a tetrahedron. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Longinetti, Marco – PersonEntity: Name: NameFull: Naldi, Simone – PersonEntity: Name: NameFull: Venturi, Adriana IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 01968858 Numbering: – Type: volume Value: 176 Titles: – TitleFull: Advances in Applied Mathematics Type: main |
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