{"id":161327,"date":"2025-08-08T14:14:48","date_gmt":"2025-08-08T11:14:48","guid":{"rendered":"https:\/\/azbuki.bg\/?p=161327"},"modified":"2025-08-08T14:14:48","modified_gmt":"2025-08-08T11:14:48","slug":"kombinatorni-zadachi-varhu-kvadratni-i-triagalni-mrezhi-sas-strunima-i-geogebra","status":"publish","type":"post","link":"https:\/\/philosophy.azbuki.bg\/en\/uncategorized\/kombinatorni-zadachi-varhu-kvadratni-i-triagalni-mrezhi-sas-strunima-i-geogebra\/","title":{"rendered":"Combinatorial Problems using Square and Triangular Grids with StruniMa and Geogebra"},"content":{"rendered":"<p><strong>Mladen Valkov<sup>1)<\/sup><\/strong><\/p>\n<p><em><sup>1)<\/sup><\/em><em>Bulgaria<\/em><\/p>\n<p><a href=\"https:\/\/doi.org\/10.53656\/math2025-3-4-cpu\" target=\"_blank\" rel=\"noopener\">https:\/\/doi.org\/10.53656\/math2025-3-4-cpu<\/a><\/p>\n<p><strong>Abstract.<\/strong> In this article we look at digital systems as Geogebra and StruniMa, with which some mathematical problems with square and triangular sets can be investigated. They are developed on the base of famous mathematical constructions as magic rectangles, competition mathematical problems and open mathematical problems (for example exact formula for the no-three-in-line problem).<\/p>\n<p><em>Keywords: <\/em>square grid; triangular grid; Geogebra; StruniMa<\/p>\n<a href=\"https:\/\/philosophy.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>","protected":false},"excerpt":{"rendered":"<p>\u041c\u043b\u0430\u0434\u0435\u043d \u0412\u044a\u043b\u043a\u043e\u04321) 1)\u0411\u044a\u043b\u0433\u0430\u0440\u0438\u044f https:\/\/doi.org\/10.53656\/math2025-3-4-cpu \u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0442\u0430\u0437\u0438 \u0441\u0442\u0430\u0442\u0438\u044f \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0434\u0438\u0433\u0438\u0442\u0430\u043b\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430, \u0447\u0440\u0435\u0437 \u043a\u043e\u0438\u0442\u043e \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0441\u0435 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u0442 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0438 \u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438 \u043c\u0440\u0435\u0436\u0438, \u043a\u043e\u0438\u0442\u043e \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0431\u044a\u0434\u0430\u0442 \u043a\u0430\u043a\u0442\u043e \u0447\u0438\u0441\u043b\u043e\u0432\u0438, \u0442\u0430\u043a\u0430 \u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438. \u0422\u0435\u043c\u0430\u0442\u0430 \u0435 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0435\u043d\u0430 \u043d\u0430 \u0431\u0430\u0437\u0430\u0442\u0430 \u043d\u0430 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0438 \u0442\u0435\u043c\u0438, \u043a\u0430\u0442\u043e \u043c\u0430\u0433\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u0440\u0430\u0432\u043e\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438, \u0441\u044a\u0441\u0442\u0435\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438, \u043a\u0430\u043a\u0442\u043e \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043e\u0442\u0432\u043e\u0440\u0435\u043d\u0438 \u0432\u044a\u043f\u0440\u043e\u0441\u0438 (\u043d\u0430\u043f\u0440. \u0442\u043e\u0447\u043d\u0430 [&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":[7598,12803,12804,12805],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ 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\u0432\u044a\u0440\u0445\u0443 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0438 \u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438 \u043c\u0440\u0435\u0436\u0438 \u0441\u044a\u0441 \u201e\u0421\u0442\u0440\u0443\u043d\u0438\u041c\u0430\u201c \u0438 Geogebra - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"\u041c\u043b\u0430\u0434\u0435\u043d \u0412\u044a\u043b\u043a\u043e\u04321) 1)\u0411\u044a\u043b\u0433\u0430\u0440\u0438\u044f https:\/\/doi.org\/10.53656\/math2025-3-4-cpu \u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0442\u0430\u0437\u0438 \u0441\u0442\u0430\u0442\u0438\u044f \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0434\u0438\u0433\u0438\u0442\u0430\u043b\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430, \u0447\u0440\u0435\u0437 \u043a\u043e\u0438\u0442\u043e \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0441\u0435 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u0442 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