The angle defect for arbitrary polyhedra (Q1267335)
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scientific article; zbMATH DE number 1208012
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The angle defect for arbitrary polyhedra |
scientific article; zbMATH DE number 1208012 |
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The angle defect for arbitrary polyhedra (English)
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21 July 1999
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The Gauss-Bonnet Theorem for surfaces uses the angle defect to measure curvature. In the present paper, by making use of a natural stratification, the angle defect is generalized to arbitrary polyhedra in all dimensions. A Gauss-Bonnet type theorem is then proved for arbitrary polyhedra in terms of a modified Euler characteristic based on this stratification. The modified Euler characteristic, in general, is different from the classical one.
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polyhedra
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Gauss-Bonnet theorem
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curvature
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stratification
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Euler characteristic
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