Total angular defect and Euler's theorem for polyhedra (Q5891789)
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scientific article; zbMATH DE number 6088972
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Total angular defect and Euler's theorem for polyhedra |
scientific article; zbMATH DE number 6088972 |
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1 October 2012
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Descartes' theorem
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Euler's theorem
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convex polyhedron
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Total angular defect and Euler's theorem for polyhedra (English)
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The authors give an inductive proof of Descartes' theorem that the total angular defect of a convex polyhedron is equal to \(4\pi\). This is well known to be equivalent to Euler's formula \(V-E+F=2\).
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