@article{14464,
abstract = {Given a triangle Δ, we study the problem of determining the smallest enclosing and largest embedded isosceles triangles of Δ with respect to area and perimeter. This problem was initially posed by Nandakumar [17, 22] and was first studied by Kiss, Pach, and Somlai [13], who showed that if Δ′ is the smallest area isosceles triangle containing Δ, then Δ′ and Δ share a side and an angle. In the present paper, we prove that for any triangle Δ, every maximum area isosceles triangle embedded in Δ and every maximum perimeter isosceles triangle embedded in Δ shares a side and an angle with Δ. Somewhat surprisingly, the case of minimum perimeter enclosing triangles is different: there are infinite families of triangles Δ whose minimum perimeter isosceles containers do not share a side and an angle with Δ.},
author = {Ambrus, Áron and Csikós, Mónika and Kiss, Gergely and Pach, János and Somlai, Gábor},
issn = {1793-6373},
journal = {International Journal of Foundations of Computer Science},
number = {7},
pages = {737--760},
publisher = {World Scientific Publishing},
title = {{Optimal embedded and enclosing isosceles triangles}},
doi = {10.1142/S012905412342008X},
volume = {34},
year = {2023},
}