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