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Minimal enclosing hyperbolas of line sets. (English) Zbl 1167.53003
Author’s abstract: We prove the following theorem: If $$H$$ is a slim hyperbola that contains a closed set $$\mathcal{S}$$ of lines in the Euclidean plane, there exists exactly one hyperbola $$H_{\min}$$ of minimal volume that contains $$\mathcal{S}$$ and is contained in $$H$$. The precise concepts of “slim”, the “volume of a hyperbola” and “straight lines or hyperbolas being contained in a hyperbola” are defined in the text.

##### MSC:
 53A04 Curves in Euclidean and related spaces
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