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If, for a double normal <italic>xx</italic>* of a convex body <italic>K</italic>, an ellipse <italic>E</italic> ∋ <italic>x, x</italic>* is included in <italic>K</italic>, we say that <italic>E</italic> is <italic>surrounded</italic> by the boundary of <italic>K</italic>. If, instead, in the plane of <italic>E</italic>, <italic>K</italic> is included in the convex hull of <italic>E</italic>, then we say that <italic>E</italic> is <italic>surrounding K</italic>. In this paper we investigate surrounding and surrounded ellipses, particularly circles. We do this for arbitrary convex bodies, for polytopes, for convex bodies of constant width, and for most convex bodies (in the sense of Baire categories).
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If, for a double normal xx* of a convex body K, an ellipse E ∋ x, x* is included in K, we say that E is surrounded by the boundary of K. If, instead, in the plane of E, K is included in the convex hull of E, then we say that E is surrounding K. In this paper we investigate surrounding and surrounded ellipses, particularly circles. We do this for arbitrary convex bodies, for polytopes, for convex bodies of constant width, and for most convex bodies (in the sense of Baire categories).

Ellipses surrounding convex bodies

tudor.zamfirescu@mathematik.uni-dortmund.de

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Ellipses surrounding convex bodies"}

If, for a double normal xx* of a convex body K, an ellipse E ∋ x, x* is included in K, we say that E is surrounded by the boundary of K. If, instead, in the...

Ellipses surrounding convex bodies

Publié en ligne: 02 juin 2022

Pages: 273 - 282

Reçu: 19 juil. 2021

Accepté: 25 sept. 2021

DOI: https://doi.org/10.2478/auom-2022-0030

Mots clés
Double normal, convex body of constant width, surrounded and surrounding ellipses

© 2022 Tudor Zamfirescu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Ellipses surrounding convex bodies

Publié en ligne: 02 juin 2022

Pages: 273 - 282

Reçu: 19 juil. 2021

Accepté: 25 sept. 2021

DOI: https://doi.org/10.2478/auom-2022-0030

Mots clésDouble normal, convex body of constant width, surrounded and surrounding ellipses

© 2022 Tudor Zamfirescu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Double normal, convex body of constant width, surrounded and surrounding ellipses