Geodesic
On a Property of $n$-Dimensional Simplices
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 580-593.

Voir la notice de l'article provenant de la source Math-Net.Ru

Suppose that $n\in\mathbb N$ and $S$ is a simplex in $\mathbb R^n$, containing the cube $[0,1]^n$. It is proved that, for some $i=1,\dots,n$, the simplex $S$ contains an interval of length $n$ parallel to the $i$th coordinate axis. The relationship with questions arising in linear interpolation of continuous functions of $n$ variables is noted.
Keywords: $n$-dimensional simplex, polytope, barycentric coordinates, axial diameter, interpolation projection operator, Steiner symmetrization, Hadamard number. 
@article{MZM_2010_87_4_a9,
     author = {M. V. Nevskij},
     title = {On a {Property} of $n${-Dimensional} {Simplices}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {580--593},
     publisher = {mathdoc},
     volume = {87},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a9/}
}
TY  - JOUR
AU  - M. V. Nevskij
TI  - On a Property of $n$-Dimensional Simplices
JO  - Matematičeskie zametki
PY  - 2010
SP  - 580
EP  - 593
VL  - 87
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a9/
LA  - ru
ID  - MZM_2010_87_4_a9
ER  - 
%0 Journal Article
%A M. V. Nevskij
%T On a Property of $n$-Dimensional Simplices
%J Matematičeskie zametki
%D 2010
%P 580-593
%V 87
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a9/
%G ru
%F MZM_2010_87_4_a9
M. V. Nevskij. On a Property of $n$-Dimensional Simplices. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 580-593. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a9/

[1] M. V. Nevskii, “Ob odnom sootnoshenii dlya minimalnoi normy interpolyatsionnogo proektora”, Model. i analiz inform. sistem, 16:1 (2009), 24–43

[2] P. S. Aleksandrov, Kurs analiticheskoi geometrii i lineinoi algebry, Nauka, M., 1979 | MR | Zbl

[3] P. R. Scott, “Lattices and convex sets in space”, Quart. J. Math. Oxford Ser. (2), 36:143 (1985), 359–362 | DOI | MR | Zbl

[4] P. R. Scott, “Properties of axial diameters”, Bull. Austral. Math. Soc., 39:3 (1989), 329–333 | DOI | MR | Zbl

[5] K. Radziszewski, “Sur un probleme extremal relatif aux figures inscrites et circonscrites aux figures convexes”, Ann. Univ. Mariae Curie-Skłodowska. Sect. A, 6 (1952), 5–18 | MR | Zbl

[6] V. Blyashke, Krug i shar, Nauka, M., 1967 | MR | Zbl

[7] M. Lassak, “Parallelotopes of maximum volume in a simplex”, Discrete Comput. Geom., 21:3 (1999), 449–462 | DOI | MR | Zbl

[8] M. Y. Balla, Approximation of convex bodies by parallelotopes, Internal report IC/87/310, International Centre for Theoretical Physics, Trieste, 1987

[9] M. V. Nevskii, “Geometricheskie metody v zadache o minimalnom proektore”, Model. i analiz inform. sistem, 13:2 (2006), 16–29