We prove that each convex body in ℝn has n pairwise orthogonal affine diameters d1, . . . , dn such that it is possible to shift each of them through a linear combination of direction vectors of the diameters with smaller numbers so that their translates will intersect at their common midpoint.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Grünbaum, Essays on Combinatorial Geometry and Theory of Convex Bodies [Russian translation], Moscow, Nauka (1971).
V. V. Makeev, “Special configurations of planes related to a convex compactum,” Zap. Nauchn. Semin. POMI, 252, 165–174 (1998).
V. V. Makeev, “On affine diameters and chords of convex compacta,” Zap. Nauchn. Semin. POMI, 299, 252–261 (2003).
V. V. Makeev, “On intersections of affine diameters of a convex body,” Ukr. Geom. Sb., 33, 70–73 (1990).
V. P. Soltan, “Affine diameters of convex bodies,” Survey Exp. Math., 23, 47–63 (2005).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 415, 2013, pp. 39–41.
Rights and permissions
About this article
Cite this article
Makeev, V.V., Zvagel’skii, M.Y. Affine Diameters of a Convex Body. J Math Sci 212, 542–543 (2016). https://doi.org/10.1007/s10958-016-2684-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-016-2684-6