On the extended \textit{Ptolomy} 's theorem in hyperbolic geometry. (Q1477587)
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scientific article; zbMATH DE number 2622447
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the extended \textit{Ptolomy} 's theorem in hyperbolic geometry. |
scientific article; zbMATH DE number 2622447 |
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On the extended \textit{Ptolomy} 's theorem in hyperbolic geometry. (English)
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1913
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Werden vier Kreise von einem fünften berührt, so ist \(t_{12}t_{34}+t_{23}t_{14}=t_{13}t_{24},\) wo \(t_{ik}\) die gemeinsame Tangente des \(i\)-ten und \(k\)-ten Kreises bedeutet (\textit{Casey,} Dublin Proc. 1866). Der Satz wird auf die hyperbolische Geometrie übertragen; an Stelle von \(t_{ik}\) tritt dann sinh \(\frac {t_{ik}}2.\) - Elegante Handhabung des analytischen Apparates.
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