---
res:
bibo_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.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Áron
foaf_name: Ambrus, Áron
foaf_surname: Ambrus
- foaf_Person:
foaf_givenName: Mónika
foaf_name: Csikós, Mónika
foaf_surname: Csikós
- foaf_Person:
foaf_givenName: Gergely
foaf_name: Kiss, Gergely
foaf_surname: Kiss
- foaf_Person:
foaf_givenName: János
foaf_name: Pach, János
foaf_surname: Pach
foaf_workInfoHomepage: http://www.librecat.org/personId=E62E3130-B088-11EA-B919-BF823C25FEA4
- foaf_Person:
foaf_givenName: Gábor
foaf_name: Somlai, Gábor
foaf_surname: Somlai
bibo_doi: 10.1142/S012905412342008X
bibo_issue: '7'
bibo_volume: 34
dct_date: 2023^xs_gYear
dct_identifier:
- UT:001080874400001
dct_isPartOf:
- http://id.crossref.org/issn/0129-0541
- http://id.crossref.org/issn/1793-6373
dct_language: eng
dct_publisher: World Scientific Publishing@
dct_title: Optimal embedded and enclosing isosceles triangles@
...