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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Some geometric properties of convex bodies. II


Author: V. V. Makeev
Translated by: N. Yu. Netsvetaev
Original publication: Algebra i Analiz, tom 15 (2003), nomer 6.
Journal: St. Petersburg Math. J. 15 (2004), 867-874
MSC (2000): Primary 52A10, 52A15
Published electronically: November 16, 2004
MathSciNet review: 2044632
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Abstract | References | Similar Articles | Additional Information

Abstract: Topological means are used for the study of approximation of $2$-dimensional sections of a $3$-dimensional convex body by affine-regular pentagons and approximation of a centrally symmetric convex body by a prism. Also, the problem of estimating the relative surface area of the sphere in a normed $3$-space, the problem on universal covers for sets of unit diameter in Euclidean space, and some related questions are considered.


References [Enhancements On Off] (What's this?)

  • 1. V. V. Makeev, The Knaster problem and almost spherical sections, Mat. Sb. 180 (1989), no. 3, 424–431 (Russian); English transl., Math. USSR-Sb. 66 (1990), no. 2, 431–438. MR 993234 (90d:55005)
  • 2. V. V. Makeev, Affine-inscribed and affine-circumscribed polygons and polyhedra, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 231 (1995), no. Issled. po Topol. 8, 286–298, 327–328 (1996) (Russian, with Russian summary); English transl., J. Math. Sci. (New York) 91 (1998), no. 6, 3518–3525. MR 1434300 (98b:52004), http://dx.doi.org/10.1007/BF02434930
  • 3. J. Pal, Über ein elementares Variationsproblem, Danske Vid. Selsk. Mat.-Fys. Medd. 3 (1920), no. 2, 35 pp.
  • 4. V. V. Makeev, On affine images of a rhombo-dodecahedron circumscribed about a three-dimensional convex body, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 246 (1997), no. Geom. i Topol. 2, 191–195, 200 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (New York) 100 (2000), no. 3, 2307–2309. MR 1631812 (99e:52005)
  • 5. V. V. Makeev, Some special configurations of planes that are associated with convex compacta, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 252 (1998), no. Geom. i Topol. 3, 165–174, 251 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (New York) 104 (2001), no. 4, 1358–1363. MR 1756722 (2001f:52013), http://dx.doi.org/10.1023/A:1011346317749
  • 6. T. Hausel, E. Makai Jr., and A. Szűcs, Polyhedra inscribed and circumscribed to convex bodies, Proceedings of the Third International Workshop on Differential Geometry and its Applications and the First German-Romanian Seminar on Geometry (Sibiu, 1997), 1997, pp. 183–190. MR 1723608
  • 7. Greg Kuperberg, Circumscribing constant-width bodies with polytopes, New York J. Math. 5 (1999), 91–100 (electronic). MR 1703205 (2000h:52002)
  • 8. V. V. Makeev, Three-dimensional polytopes inscribed in and circumscribed about convex compacta, Algebra i Analiz 12 (2000), no. 4, 1–15 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 12 (2001), no. 4, 507–518. MR 1793615 (2001k:52017)
  • 9. V. V. Makeev, Universal coverings. I, Ukrain. Geom. Sb. 24 (1981), 70–79, iii (Russian). MR 629813 (83e:52009)
  • 10. V. V. Makeev, On some geometric properties of three-dimensional convex bodies, Algebra i Analiz 14 (2002), no. 5, 96–109 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 14 (2003), no. 5, 781–790. MR 1970335 (2004c:52001)
  • 11. V. V. Makeev, Inscribed and circumscribed polygons of a convex body, Mat. Zametki 55 (1994), no. 4, 128–130 (Russian); English transl., Math. Notes 55 (1994), no. 3-4, 423–425. MR 1296224 (95h:52002), http://dx.doi.org/10.1007/BF02112484

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Additional Information

V. V. Makeev
Affiliation: Universitetskiĭ Pr. 27, St. Petersburg 190000, Russia

DOI: http://dx.doi.org/10.1090/S1061-0022-04-00836-2
PII: S 1061-0022(04)00836-2
Keywords: Convex body, figure, field of convex bodies, relative surface area
Received by editor(s): December 25, 2002
Published electronically: November 16, 2004
Additional Notes: The paper was revised by the author for the English edition.
Article copyright: © Copyright 2004 American Mathematical Society



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