A Stereological Version of the Gauss–Bonnet Formula

Authors: Gual-Arnau X.¹; Nuño-Ballesteros J.J.²

Source: Geometriae Dedicata, Volume 84, Numbers 1-3, February 2001 , pp. 253-260(8)

Publisher: Springer

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Abstract:

We give a stereological version of the Gauss–Bonnet formula in order to compute the Euler characteristic of a domain with boundary in a smooth orientable surface in \Bbb R^3, by looking at contacts with a ‘sweeping’ plane.

Keywords: Euler–Poincare characteristic; contact with planes

Language: English

Document Type: Regular paper

Affiliations: 1: Department de Matemàtiques, Campus Riu Sec, Universitat Jaume I, 12071 Castelló, Spain. E-mail: gual@mat.uji.es 2: Departament de Geometria i Topologia, Universitat de València, Campus de Burjassot, 46100 Burjassot, Spain. E-mail: nuno@uv.es

Publication date: 2001-02-01