Minimal Area Tetrahedron Circumscribing a Strictly Convex Body in ℝ^3

Andrzej Miernowski; Witold Mozgawa; Witold Rzymowski

doi:10.68381/jca14003

Abstract

We are interested in the geometric characterization of tangency points of a minimal area tetrahedron circumscribed around a strictly convex compact body in

\mathbb{R}^3

.

Author information

Contact details are reproduced from the original publication and may be historical.

Andrzej Miernowski

Instytut Matematyki, Uniwersytet M. Curie-Skłodowskiej, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland

mierand@golem.umcs.lublin.pl

Witold Mozgawa

Instytut Matematyki, Uniwersytet M. Curie-Skłodowskiej, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland

mozgawa@golem.umcs.lublin.pl

Witold Rzymowski

Instytut Matematyki, Uniwersytet M. Curie-Skłodowskiej, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland

witrz@golem.umcs.lublin.pl

Keywords

Tetrahedron
Lagrange multiplier
circumscribing
homothety

Mathematics Subject Classification

52A15, 53A05

References

W. Cieślak, M. Maksym, D. DeTemple: On polygons circumscribing a closed convex curve, J. Geom. 40 (1991) 26–34.https://doi.org/10.1007/BF01225869 Google Scholar
W. Cieślak, S. Góźdź: Extremal polygons circumscribed an oval, Acta Math. Hung. 54(1-2) (1989) 63–68.https://doi.org/10.1007/BF01950710 Google Scholar
W. Cieślak: Regular polygons circumscribing a convex body, Bull. Pol. Acad. Sci., Math. 45 (1997) 263–268.Google Scholar
M. M. Day: Polygons circumscribed about closed convex curves, Trans. Amer. Math. Soc. 62 (1947) 315–319.https://doi.org/10.1090/S0002-9947-1947-0022686-9 Google Scholar
M. Levi: Minimal perimeter triangles, Amer. Math. Mon. 109 (2002) 890–899.https://doi.org/10.1080/00029890.2002.11919926 Google Scholar
R. T. Rockafellar: Convex Analysis, Princeton University Press, Princeton (1970).https://doi.org/10.1515/9781400873173 Google Scholar
L. F. Toth: Lagerungen in der Ebene auf der Kugel und im Raum, Springer, Berlin (1953).https://doi.org/10.1007/978-3-662-01206-2 Google Scholar

Suggested citation

Published by Heldermann Verlag, 2007. Rights now held by Banach Press LLC.

[1] W. Cieślak, M. Maksym, D. DeTemple: On polygons circumscribing a closed convex curve, J. Geom. 40 (1991) 26–34.https://doi.org/10.1007/BF01225869 Google Scholar

[2] W. Cieślak, S. Góźdź: Extremal polygons circumscribed an oval, Acta Math. Hung. 54(1-2) (1989) 63–68.https://doi.org/10.1007/BF01950710 Google Scholar

[3] W. Cieślak: Regular polygons circumscribing a convex body, Bull. Pol. Acad. Sci., Math. 45 (1997) 263–268.Google Scholar

[4] M. M. Day: Polygons circumscribed about closed convex curves, Trans. Amer. Math. Soc. 62 (1947) 315–319.https://doi.org/10.1090/S0002-9947-1947-0022686-9 Google Scholar

[5] M. Levi: Minimal perimeter triangles, Amer. Math. Mon. 109 (2002) 890–899.https://doi.org/10.1080/00029890.2002.11919926 Google Scholar

[6] R. T. Rockafellar: Convex Analysis, Princeton University Press, Princeton (1970).https://doi.org/10.1515/9781400873173 Google Scholar

[7] L. F. Toth: Lagerungen in der Ebene auf der Kugel und im Raum, Springer, Berlin (1953).https://doi.org/10.1007/978-3-662-01206-2 Google Scholar