{"id":149021,"date":"2025-04-04T11:30:33","date_gmt":"2025-04-04T08:30:33","guid":{"rendered":"https:\/\/azbuki.bg\/?p=149021"},"modified":"2025-04-04T11:30:33","modified_gmt":"2025-04-04T08:30:33","slug":"applying-delaunay-triangulation-in-olympiad-problems","status":"publish","type":"post","link":"https:\/\/vocedu.azbuki.bg\/en\/uncategorized\/applying-delaunay-triangulation-in-olympiad-problems\/","title":{"rendered":"Applying Delaunay Triangulation in Olympiad Problems"},"content":{"rendered":"<p><strong>Dragomir Grozev, Nevena Sybeva<\/strong><br \/>\n<em>Institute of Mathematics and Informatics<\/em><br \/>\nBulgarian Academy of Sciences \u2013 Sofia (Bulgaria)<\/p>\n<p><a href=\"https:\/\/doi.org\/10.53656\/math2025-1-1-app\" target=\"_blank\" rel=\"noopener\">https:\/\/doi.org\/10.53656\/math2025-1-1-app<\/a><\/p>\n<p><strong>Abstract.<\/strong> Some fundamental properties of Delaunay triangulation are presented in this article. The construction of the triangulation described here has not been encountered by the authors in the known literature. The main point is to apply this triangulation in solving otherwise challenging Olympiad problems in combinatorial geometry. One of the problems in which the method is applied is from the \u2019Mikl\u00b4os Schweitzer\u2019 competition, 2002. It is extremely difficult without knowing the Delaunay triangulation properties.<br \/>\nThe second problem illustrating the method is from a prestigious Russian 239 competition held in 2024. The third is from the USA team selection tests for the IMO 2024.<br \/>\n<em>Keywords:<\/em> Delaunay triangulation, combinatorial geometry, coloring, perfect matching, Mikl\u00b4os Schweitzer competition<\/p>\n<a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>","protected":false},"excerpt":{"rendered":"<p>Dragomir Grozev, Nevena Sybeva Institute of Mathematics and Informatics Bulgarian Academy of Sciences \u2013 Sofia (Bulgaria) https:\/\/doi.org\/10.53656\/math2025-1-1-app Abstract. Some fundamental properties of Delaunay triangulation are presented in this article. The construction of the triangulation described here has not been encountered by the authors in the known literature. The main point is to apply this triangulation [&hellip;]<\/p>","protected":false},"author":124332423427287,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[]},"categories":[1],"tags":[10653,10652,10651,10655,10654],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Applying Delaunay Triangulation in Olympiad Problems - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/vocedu.azbuki.bg\/en\/uncategorized\/applying-delaunay-triangulation-in-olympiad-problems\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Applying Delaunay Triangulation in Olympiad Problems - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"Dragomir Grozev, Nevena Sybeva Institute of Mathematics and Informatics Bulgarian Academy of Sciences \u2013 Sofia (Bulgaria) https:\/\/doi.org\/10.53656\/math2025-1-1-app Abstract. Some fundamental properties of Delaunay triangulation are presented in this article. The construction of the triangulation described here has not been encountered by the authors in the known literature. The main point is to apply this triangulation [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/vocedu.azbuki.bg\/en\/uncategorized\/applying-delaunay-triangulation-in-olympiad-problems\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Azbuki55\/\" \/>\n<meta property=\"article:published_time\" content=\"2025-04-04T08:30:33+00:00\" \/>\n<meta name=\"author\" content=\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/uncategorized\/applying-delaunay-triangulation-in-olympiad-problems\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/uncategorized\/applying-delaunay-triangulation-in-olympiad-problems\/\"},\"author\":{\"name\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\",\"@id\":\"https:\/\/azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd\"},\"headline\":\"Applying Delaunay Triangulation in Olympiad Problems\",\"datePublished\":\"2025-04-04T08:30:33+00:00\",\"dateModified\":\"2025-04-04T08:30:33+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/uncategorized\/applying-delaunay-triangulation-in-olympiad-problems\/\"},\"wordCount\":167,\"publisher\":{\"@id\":\"https:\/\/azbuki.bg\/en\/#organization\"},\"keywords\":[\"coloring\",\"combinatorial geometry\",\"Delaunay triangulation\",\"Mikl\u00b4os Schweitzer competition\",\"perfect matching\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/uncategorized\/applying-delaunay-triangulation-in-olympiad-problems\/\",\"url\":\"https:\/\/vocedu.azbuki.bg\/en\/uncategorized\/applying-delaunay-triangulation-in-olympiad-problems\/\",\"name\":\"Applying Delaunay Triangulation in Olympiad Problems - 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