A stereological version of the Gauss-Bonnet formula (Q5933883)
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scientific article; zbMATH DE number 1604968
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A stereological version of the Gauss-Bonnet formula |
scientific article; zbMATH DE number 1604968 |
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A stereological version of the Gauss-Bonnet formula (English)
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6 November 2001
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The authors derive a formula for the Euler characteristic of a domain \(D\) with boundary lying on a smooth oriented surface in 3-space. They show that - for a generic direction \(u\) - the Euler characteristic can be obtained by summing certain indices of intersection for all points of first order contact of \(D\) and its boundary with the planes normal to \(u\).
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Euler characteristic
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domain with boundary
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smooth oriented surface in 3-space
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points of first order contact
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0.89462686
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0.89244336
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0.8887827
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0.88803625
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0.8863621
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