---
_id: '14464'
abstract:
- lang: eng
  text: '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.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Áron
  full_name: Ambrus, Áron
  last_name: Ambrus
- first_name: Mónika
  full_name: Csikós, Mónika
  last_name: Csikós
- first_name: Gergely
  full_name: Kiss, Gergely
  last_name: Kiss
- first_name: János
  full_name: Pach, János
  id: E62E3130-B088-11EA-B919-BF823C25FEA4
  last_name: Pach
- first_name: Gábor
  full_name: Somlai, Gábor
  last_name: Somlai
citation:
  ama: Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. Optimal embedded and enclosing
    isosceles triangles. <i>International Journal of Foundations of Computer Science</i>.
    2023;34(7):737-760. doi:<a href="https://doi.org/10.1142/S012905412342008X">10.1142/S012905412342008X</a>
  apa: Ambrus, Á., Csikós, M., Kiss, G., Pach, J., &#38; Somlai, G. (2023). Optimal
    embedded and enclosing isosceles triangles. <i>International Journal of Foundations
    of Computer Science</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/S012905412342008X">https://doi.org/10.1142/S012905412342008X</a>
  chicago: Ambrus, Áron, Mónika Csikós, Gergely Kiss, János Pach, and Gábor Somlai.
    “Optimal Embedded and Enclosing Isosceles Triangles.” <i>International Journal
    of Foundations of Computer Science</i>. World Scientific Publishing, 2023. <a
    href="https://doi.org/10.1142/S012905412342008X">https://doi.org/10.1142/S012905412342008X</a>.
  ieee: Á. Ambrus, M. Csikós, G. Kiss, J. Pach, and G. Somlai, “Optimal embedded and
    enclosing isosceles triangles,” <i>International Journal of Foundations of Computer
    Science</i>, vol. 34, no. 7. World Scientific Publishing, pp. 737–760, 2023.
  ista: Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. 2023. Optimal embedded and enclosing
    isosceles triangles. International Journal of Foundations of Computer Science.
    34(7), 737–760.
  mla: Ambrus, Áron, et al. “Optimal Embedded and Enclosing Isosceles Triangles.”
    <i>International Journal of Foundations of Computer Science</i>, vol. 34, no.
    7, World Scientific Publishing, 2023, pp. 737–60, doi:<a href="https://doi.org/10.1142/S012905412342008X">10.1142/S012905412342008X</a>.
  short: Á. Ambrus, M. Csikós, G. Kiss, J. Pach, G. Somlai, International Journal
    of Foundations of Computer Science 34 (2023) 737–760.
date_created: 2023-10-29T23:01:18Z
date_published: 2023-10-05T00:00:00Z
date_updated: 2023-12-13T13:04:55Z
day: '05'
department:
- _id: HeEd
doi: 10.1142/S012905412342008X
external_id:
  arxiv:
  - '2205.11637'
  isi:
  - '001080874400001'
intvolume: '        34'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2205.11637
month: '10'
oa: 1
oa_version: Preprint
page: 737-760
publication: International Journal of Foundations of Computer Science
publication_identifier:
  eissn:
  - 1793-6373
  issn:
  - 0129-0541
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal embedded and enclosing isosceles triangles
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2023'
...