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.


53A04 Curves in Euclidean and related spaces
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