{"date_created":"2018-12-11T11:49:09Z","month":"01","citation":{"apa":"Akopyan, A., &#38; Vysotsky, V. (2017). On the lengths of curves passing through boundary points of a planar convex shape. <i>The American Mathematical Monthly</i>. Mathematical Association of America. <a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">https://doi.org/10.4169/amer.math.monthly.124.7.588</a>","chicago":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” <i>The American Mathematical Monthly</i>. Mathematical Association of America, 2017. <a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">https://doi.org/10.4169/amer.math.monthly.124.7.588</a>.","ista":"Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.","ieee":"A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary points of a planar convex shape,” <i>The American Mathematical Monthly</i>, vol. 124, no. 7. Mathematical Association of America, pp. 588–596, 2017.","short":"A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.","ama":"Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points of a planar convex shape. <i>The American Mathematical Monthly</i>. 2017;124(7):588-596. doi:<a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">10.4169/amer.math.monthly.124.7.588</a>","mla":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” <i>The American Mathematical Monthly</i>, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96, doi:<a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">10.4169/amer.math.monthly.124.7.588</a>."},"article_processing_charge":"No","department":[{"_id":"HeEd"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["000413947300002"],"arxiv":["1605.07997"]},"page":"588 - 596","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"status":"public","isi":1,"publication_identifier":{"issn":["00029890"]},"type":"journal_article","volume":124,"date_updated":"2023-10-17T11:24:57Z","abstract":[{"text":"We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor &amp;#xbd; cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape.","lang":"eng"}],"publication":"The American Mathematical Monthly","publication_status":"published","author":[{"first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Vladislav","full_name":"Vysotsky, Vladislav","last_name":"Vysotsky"}],"doi":"10.4169/amer.math.monthly.124.7.588","_id":"909","date_published":"2017-01-01T00:00:00Z","day":"01","ec_funded":1,"article_type":"original","publisher":"Mathematical Association of America","year":"2017","language":[{"iso":"eng"}],"intvolume":"       124","publist_id":"6534","oa_version":"Submitted Version","issue":"7","title":"On the lengths of curves passing through boundary points of a planar convex shape","scopus_import":"1","quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1605.07997","open_access":"1"}]}