Isoradial bodies

René Brandenberg; Abhi Dattasharma; Peter Gritzmann; David Larman

doi:10.1007/s00454-004-1132-4

Isoradial bodies

René Brandenberg, Abhi Dattasharma, Peter Gritzmann, David Larman

Chair of Geometry

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper we show that for any dimension d ≥ 2 there exists a non-spherical strongly isoradial body, i.e., a non-spherical body of constant breadth, such that its orthogonal projections on any subspace has constant in- and circumradius. Besides the curiosity aspect of these bodies, they are highly relevant for the analysis of geometric inequalities between the radii and their extreme cases.

Original language	English
Pages (from-to)	447-457
Number of pages	11
Journal	Discrete and Computational Geometry
Volume	32
Issue number	4
DOIs	https://doi.org/10.1007/s00454-004-1132-4
State	Published - Nov 2004

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title = "Isoradial bodies",

abstract = "In this paper we show that for any dimension d ≥ 2 there exists a non-spherical strongly isoradial body, i.e., a non-spherical body of constant breadth, such that its orthogonal projections on any subspace has constant in- and circumradius. Besides the curiosity aspect of these bodies, they are highly relevant for the analysis of geometric inequalities between the radii and their extreme cases.",

author = "Ren{\'e} Brandenberg and Abhi Dattasharma and Peter Gritzmann and David Larman",

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doi = "10.1007/s00454-004-1132-4",

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AU - Brandenberg, René

AU - Dattasharma, Abhi

AU - Gritzmann, Peter

AU - Larman, David

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Y1 - 2004/11

N2 - In this paper we show that for any dimension d ≥ 2 there exists a non-spherical strongly isoradial body, i.e., a non-spherical body of constant breadth, such that its orthogonal projections on any subspace has constant in- and circumradius. Besides the curiosity aspect of these bodies, they are highly relevant for the analysis of geometric inequalities between the radii and their extreme cases.

AB - In this paper we show that for any dimension d ≥ 2 there exists a non-spherical strongly isoradial body, i.e., a non-spherical body of constant breadth, such that its orthogonal projections on any subspace has constant in- and circumradius. Besides the curiosity aspect of these bodies, they are highly relevant for the analysis of geometric inequalities between the radii and their extreme cases.

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DO - 10.1007/s00454-004-1132-4

M3 - Article

AN - SCOPUS:12144253272

SN - 0179-5376

VL - 32

SP - 447

EP - 457

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 4

ER -

Isoradial bodies

Abstract

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