Bibliographic Details
| Title: |
R-hulloid of the vertices of a tetrahedron. |
| 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] |
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| Database: |
Engineering Source |
