Translative covering by homothetic copies

Bálint, Vojtech; Bálintová, A.; Branická, M.; Grešák, Pavol; Hrinko, I.; Novotný, Pavel; Stacho, M.

doi:10.1007/bf01264916

Search citation statements

Order By: Relevance

Paper Sections

Select...

Mathematics Subject Classifications (1991) 52a271

Every Simplex Inscribed In D Which Is Not Of the Form C1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1994

2011

Publication Types

Select...

Article4

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case n = 2, it is proved in [1] that hT(Q) < 3(v/~ -1)/4 for a triangle T, In this paper we deal with a similar estimate in E 3. It seems that the present method cannot be applied for higher dimensions.…”

Section: Mathematics Subject Classifications (1991) 52a27mentioning

confidence: 90%

Approximation of convex bodies by simplices

Novotný¹

1994

Geom Dedicata

View full text Add to dashboard Cite

show abstract

Section: Mathematics Subject Classifications (1991) 52a27mentioning

confidence: 90%

Approximation of convex bodies by simplices

Novotný¹

1994

Geom Dedicata

View full text Add to dashboard Cite

show abstract

“…For n = 2 the successive upper estimates 2.5, 2.34 and 2.25 on δ(C, S) were presented in ; Bálint et al (1993) and Fleicher et al (1992). We conjecture that δ(C, S) ≤ 1 + 1 2 √ 5 (≈ 2.118) for every C ∈ C 2 with the equality only for the regular pentagon P. For a position of t (S) with respect to P such that t (S) ⊂ P ⊂ 1 + 1 2 √ 5 t (S) see Fig.…”

Section: Every Simplex Inscribed In D Which Is Not Of the Form Cmentioning

confidence: 99%

Approximation of convex bodies by inscribed simplices of maximum volume

Lassak

2011

Beitr Algebra Geom

View full text Add to dashboard Cite

The Banach-Mazur distance between an arbitrary convex body and a simplex in Euclidean n-space E n is at most n +2. We obtain this estimate as an immediate consequence of our theorem which says that for an arbitrary convex body C in E n and for any simplex S of maximum volume contained in C the homothetical copy of S with ratio n + 2 and center in the barycenter of S contains C. In general, this ratio cannot be improved, as it follows from the example of any double-cone.Denote by C n the family of all convex bodies and by M n the family of all centrally symmetric convex bodies in Euclidean n-dimensional space E n .Finding simplices of large volume in convex bodies has a long history. See, for instance, the papers by Blaschke (1917) on the maximum area of triangles in planar convex bodies, by MacKinney McKinney (1974) on simplices of maximum volume in centrally symmetric convex bodies, and the survey article Hudelson et al. (1996) by Hudelson, Klee and Larman on simplices of large volume in cubes.Let A be an (n − 1)-dimensional convex body and let I = ab be a perpendicular to the hyperplane containing A non-degenerated segment centered at a point of A. We call the convex hull conv(A ∪ I ) the double pyramid with base A and apices a and b. If B is a ball of E n − 1 in place of A and if the centers of B and I coincide, the double-pyramid is called a double-cone.

show abstract

Untitled

Januszewski¹

2001

Acta Mathematica Hungarica

View full text Add to dashboard Cite

Translative covering by homothetic copies

Cited by 4 publications

References 6 publications

Approximation of convex bodies by simplices

Approximation of convex bodies by simplices

Approximation of convex bodies by inscribed simplices of maximum volume

Untitled

Contact Info

Product

Resources

About