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J. Found. Comput. Sci."],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:p> Given a triangle [Formula: see text], we study the problem of determining the smallest enclosing and largest embedded isosceles triangles of [Formula: see text] 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 [Formula: see text] is the smallest area isosceles triangle containing [Formula: see text], then [Formula: see text] and [Formula: see text] share a side and an angle. In the present paper, we prove that for any triangle [Formula: see text], every maximum area isosceles triangle embedded in [Formula: see text] and every maximum perimeter isosceles triangle embedded in [Formula: see text] shares a side and an angle with [Formula: see text]. Somewhat surprisingly, the case of minimum perimeter enclosing triangles is different: there are infinite families of triangles [Formula: see text] whose minimum perimeter isosceles containers do not share a side and an angle with [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s012905412342008x","type":"journal-article","created":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T15:34:02Z","timestamp":1696520042000},"page":"737-760","source":"Crossref","is-referenced-by-count":0,"title":["Optimal Embedded and Enclosing Isosceles Triangles"],"prefix":"10.1142","volume":"34","author":[{"given":"\u00c1ron","family":"Ambrus","sequence":"first","affiliation":[{"name":"Budapest, 1111 Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8922-6986","authenticated-orcid":false,"given":"M\u00f3nika","family":"Csik\u00f3s","sequence":"additional","affiliation":[{"name":"Department of Theoretical Computer Science, Universit\u00e9 Paris Cit\u00e9 8 Pl. 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