Skip to main content

Approximation of convex bodies by rectangles


For every plane convex body there is a pair of inscribed and circumscribed homothetic rectangles. The positive ratio of homothety is not greater than 2.

This is a preview of subscription content, access via your institution.


  1. 1.

    Asplund, E., ‘Comparison between plane symmetric vonvex bodies and parallelograms’,Math. Scand. 7 (1960), 171–180.

    Google Scholar 

  2. 2.

    Chakerian, G. D. and Stein, S. K., ‘Some intersection properties of convex bodies’,Proc. Amer. Math. Soc. 18 (1967), 109–112.

    Google Scholar 

  3. 3.

    Eggleston, H. D.,Convexity, Cambridge University Press, Cambridge, 1969.

    Google Scholar 

  4. 4.

    Grünbaum, B., ‘Measures of symmetry for convex sets’, inConvexity, Proceedings of Symposia in Pure Mathematics 7, American Mathematical Society, Providence, 1963, pp. 233–270.

    Google Scholar 

  5. 5.

    Hadwiger, H., ‘Volumschätzung für die einen Eikörper überdeckenden und unterdeckenden Parallelotope’,Elem. Math. 10 (1955), 122–124.

    Google Scholar 

  6. 6.

    John, F., ‘Extremum problems with inequalities as subsidiary conditions’,Studies and Essays presented to R. Courant, New York, 1948, pp. 187–204.

  7. 7.

    Kosiński, A., ‘A proof of an Auerbach-Banach-Mazur-Ulam theorem on convex bodies’,Colloq. Math. 17 (1957), 216–218.

    Google Scholar 

  8. 8.

    Lassak, M., ‘Approximation of plane convex bodies by centrally symmetric convex bodies’,J. London Math. Soc. (2) 40 (1989), 369–377.

    Google Scholar 

  9. 9.

    Lassak, M., ‘Approximation of convex bodies by parallelotopes’,Bull. Polish Acad. Math. 39 (1991), 219–223.

    Google Scholar 

  10. 10.

    Pólya, G. and Szegö, G., ‘Isoperimetric inequalities in mathematical physics’,Ann. Math. Stud. 27 (1951).

  11. 11.

    Radziszewski, K., ‘Sur une problème extrémal relatif aux figures inscrites et circonscrites aux figures convexes’,Ann. Univ. Mariae Curie-Sklodowska, Sect A 6 (1952), 5–18.

    Google Scholar 

Download references

Author information



Additional information

Research supported in part by Komitet Badan Naukowych (Committee of Scientific Research), grant number 2 2005 92 03.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lassak, M. Approximation of convex bodies by rectangles. Geom Dedicata 47, 111–117 (1993).

Download citation


  • Convex Body
  • Positive Ratio
  • Plane Convex
  • Plane Convex Body