@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},
}