Skip to main content
SpringerLink
Log in

Some Inequalities for Two Simplices

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

In this paper, we establish some inequalities for two n-dimensional simplices in the n-dimensional Euclidean space E n.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bottema, O. and Klamkin, M. S.: Joint triangle inequalities, Simon Stevin 48 (1975), 3–8.

    Google Scholar 

  2. Pedoe, D.: An inequality for two triangles, Proc. Cambridge Philos, Soc. 38 (1942), 397–398.

    Google Scholar 

  3. Pedoe, D.: Problem E 1562, Amer. Math. Monthly 70 (1963), 1012.

    Google Scholar 

  4. Pedoe, D.: Thinking geometrically, Amer. Math. Monthly 77 (1970), 711–721.

    Google Scholar 

  5. Pedoe, D.: Inside-outside: the Neuberg-Pedoe inequality, Univ. Beograd. Publ. Elektrotechn. Fak. Ser. Mat. Fiz., No 544–576 (1976), 95–97.

  6. Carlitz, L.: An inequality involving the areas of two triangles, Amer. Math. Monthly, 78 (1971), 772.

    Google Scholar 

  7. Chia-Kuei, P.: Sharpening the Neuberg-Pedoe inequality I, Crux. Math. 10 (1984), 68–69.

    Google Scholar 

  8. Yang, L. and Zhang, J. Z.: A generalization to several dimensions of the Neuberg-Pedoe inequality with applications, Bull. Austral. Math. Soc., 27 (1983), 203–214.

    Google Scholar 

  9. Leng, G. S.: Inequalities for edge lengths and volumes of two simplexes, Geom. Dedicata 68 (1997), 43–48.

    Google Scholar 

  10. Oppenheim, A.: Inequalities involving elements of triangles, quadrilaterals or tetrahedra, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz, No. 461–497 (1974), 256–263.

  11. Yang, L.: An application of the Cayley theorem, Shuxue Tongbao 6 (1981), 29–30 (in Chinese).

    Google Scholar 

  12. Mitrinovic, D. S., Pecaric, J. E. and Volenec, V.: Recent Advances in Geometric Inequalities, Kluwer Acad. Publ., Dordrecht, 1989.

    Google Scholar 

  13. Su, H. M.: A class of geometric inequalities for a finite set of points on a sphere, Chinese Ann. Math. Ser. A 15 (1994), 46–49 (in Chinese) (Math. Reviews 95b:51022).

    Google Scholar 

  14. Yang, S. G.: A geometric inequality for a ¢nite set of points on a sphere and its applications. Geom. Dedicata 62 (1996), 157–160.

    Google Scholar 

  15. Korchmaros, G.: Una limitazione per il volume di un simplesso n-dimensional avente spigoli di date lunghezze, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur(8) 56 (1974), 876–879.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Yueyang Normal University, Yueyang, 414000, Hunan, People's Republic of China

    Sun Mingbao

Authors
  1. Sun Mingbao
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mingbao, S. Some Inequalities for Two Simplices. Geometriae Dedicata 85, 53–67 (2001). https://doi.org/10.1023/A:1010392410168

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010392410168

Search

Navigation