{"id":42205,"date":"2017-10-16T14:37:44","date_gmt":"2017-10-16T11:37:44","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016-2\/5-lx-2017\/"},"modified":"2019-06-24T17:33:14","modified_gmt":"2019-06-24T14:33:14","slug":"5-lx-2017","status":"publish","type":"post","link":"https:\/\/foreignlanguages.azbuki.bg\/en\/matematics\/matharticles2016-2\/5-lx-2017\/","title":{"rendered":"Mathematics and Informatics, Number 5\/2017, Volume 60"},"content":{"rendered":"<p><strong><a name=\"top\"><\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418<\/strong><br \/><a href=\"#art01\">\u0418\u043d\u0442\u0435\u0433\u0440\u0430\u0442\u0438\u0432\u043d\u0438 \u0432\u0440\u044a\u0437\u043a\u0438 \u0432 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u043d\u0438\u044f \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438\u0438 <\/a><br \/><a href=\"#art01\">[Information Integrative Relationships in the Competent Approach in Mathematics Technology Training] <\/a><br \/>\/ \u041a\u043e\u0441\u0442\u0430 \u0413\u044a\u0440\u043e\u0432, \u0421\u0435\u0432\u0434\u0430\u043b\u0438\u043d\u0430 \u0413\u0435\u043e\u0440\u0433\u0438\u0435\u0432\u0430, \u0415\u043b\u0435\u043d\u0430 \u041a\u043e\u0432\u0430\u0447\u0435\u0432\u0430, \u0410\u043d\u0433\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432 \/ Kosta Garov, Sevdalina Georgieva, Elena Kovacheva, Angel Angelov &#8211; \u0441\u0442\u0440. 439<br \/><a href=\"https:\/\/foreignlanguages.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art02\">\u041d\u044f\u043a\u043e\u0438 \u043d\u0430\u0447\u0438\u043d\u0438 \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 <\/a><br \/><a href=\"#art02\">[Some Ways in Solving Algebraic Problems] <\/a><br \/>\/ \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430 \/ Diana Stefanova &#8211; \u0441\u0442\u0440. 450<br \/><a href=\"https:\/\/foreignlanguages.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art03\">\u0412\u0442\u043e\u0440\u043e\u0439 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u044b\u0439 \u0441\u0435\u0442\u0435\u0432\u043e\u0439 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u0438\u0439 \u043f\u0440\u043e\u0435\u043a\u0442 \u0443\u0447\u0430\u0449\u0438\u0445\u0441\u044f \u0432 \u0440\u0430\u043c\u043a\u0430\u0445 MITE <\/a><br \/><a href=\"#art03\">[Second International Net Research Student Project in the Frames of MITE] <\/a><br \/>\/ \u041c\u0430\u0440\u0438\u044f \u0428\u0430\u0431\u0430\u043d\u043e\u0432\u0430, \u041c\u0430\u0440\u0438\u043d\u0430 \u0411\u0435\u043b\u043e\u0440\u0443\u043a\u043e\u0432\u0430, \u0420\u043e\u0437\u0430 \u0410\u0442\u0430\u043c\u0443\u0440\u0430\u0442\u043e\u0432\u0430, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Maria Shabanova, Marina Belorukova, Roza Atamuratova, Veselin Nenkov &#8211; \u0441\u0442\u0440. 457<br \/><a href=\"https:\/\/foreignlanguages.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art04\">\u0414\u0438\u0434\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u0446\u0435\u043d\u0430\u0440\u0438\u0439 \u0432\u044a\u0440\u0445\u0443 \u0435\u0434\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u0442 XXI \u043c\u043b\u0430\u0434\u0435\u0436\u043a\u0430 \u0431\u0430\u043b\u043a\u0430\u043d\u0441\u043a\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 <\/a><br \/><a href=\"#art04\">[Didactic Scenario on a Problem from the 21st Junior Balkan Mathematical Olympiad] <\/a><br \/>\/ \u0411\u043e\u0440\u0438\u0441\u043b\u0430\u0432 \u041b\u0430\u0437\u0430\u0440\u043e\u0432 \/ Borislav Lazarov &#8211; \u0441\u0442\u0440. 466<br \/><a href=\"https:\/\/foreignlanguages.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><strong>EDUCATIONAL TECHNOLOGIES \/ \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418<\/strong><br \/><a href=\"#art05\">Some Numerical Sequences Concerning Square Roots (Part One) <\/a><br \/><a href=\"#art05\">[\u0427\u0438\u0441\u043b\u043e\u0432\u0438 \u0440\u0435\u0434\u0438\u0446\u0438, \u0441\u0432\u044a\u0440\u0437\u0430\u043d\u0438 \u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u0438 \u043a\u043e\u0440\u0435\u043d\u0438 (\u043f\u044a\u0440\u0432\u0430 \u0447\u0430\u0441\u0442)] <\/a><br \/>\/ Rosen Nikolaev, Tanka Milkova, Yordan Petkov &#8211; \u0441\u0442\u0440. 474<br \/><a href=\"https:\/\/foreignlanguages.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art06\">\u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430 \u0438 \u0443\u0442\u043e\u0447\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u043e \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u0442\u0435 \u0442\u0432\u044a\u0440\u0434\u0435\u043d\u0438\u044f \u0447\u0440\u0435\u0437 \u043f\u0440\u0438\u043d\u0446\u0438\u043f\u0430 \u0437\u0430 \u0434\u0443\u0430\u043b\u043d\u043e\u0441\u0442 <\/a><br \/><a href=\"#art06\">[Proofs and Specifications of Experimentally Derived Assertions by the Duality Principle] <\/a><br \/>\/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Sava Grozdev, Veselin Nenkov &#8211; \u0441\u0442\u0440. 481<br \/><a href=\"https:\/\/foreignlanguages.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art07\">Erd\u00f6s\u2019 Distinct Distances Problem <\/a><br \/><a href=\"#art07\">[\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044a\u0442 \u043d\u0430 \u0415\u0440\u0434\u044c\u043e\u0448 \u0437\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438\u0442\u0435 \u0440\u0430\u0437\u0441\u0442\u043e\u044f\u043d\u0438\u044f] <\/a><br \/>\/ Houssam Zenati &#8211; \u0441\u0442\u0440. 501<br \/><a href=\"https:\/\/foreignlanguages.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art08\">Optimizing the Positioning of Serving Units in Tourism Business <\/a><br \/><a href=\"#art08\">[\u041e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u044f \u043d\u0430 \u043f\u043e\u0437\u0438\u0446\u0438\u043e\u043d\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043e\u0431\u0441\u043b\u0443\u0436\u0432\u0430\u0449\u0438 \u0435\u0434\u0438\u043d\u0438\u0446\u0438 \u0432 \u0442\u0443\u0440\u0438\u0441\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u044f \u0431\u0438\u0437\u043d\u0435\u0441] <\/a><br \/>\/ Radan Miryanov, Velina Yordanova &#8211; \u0441\u0442\u0440. 515<br \/><a href=\"https:\/\/foreignlanguages.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><strong>CONTEST PROBLEMS \/ \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><br \/>Contest Problems of this Issue <br \/>[Contest Problems of This Issue] &#8211; \u0441\u0442\u0440. 521<br \/><a href=\"https:\/\/foreignlanguages.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p>\u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u043e\u0442 \u0431\u0440\u043e\u0439 6, 2016 <br \/>[Solutions of the Contest Problems from Issue 6, 2016] &#8211; \u0441\u0442\u0440. 523<br \/><a href=\"https:\/\/foreignlanguages.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><strong>READ IN THE LATEST ISSUES OF \u201eAZBUKI\u201c JOURNALS \/ \u0412 \u041d\u041e\u0412\u0418\u0422\u0415 \u0411\u0420\u041e\u0415\u0412\u0415 \u041d\u0410 \u0421\u041f\u0418\u0421\u0410\u041d\u0418\u042f\u0422\u0410 \u041d\u0410 \u0418\u0417\u0414\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u041e \u201e\u0410\u0417\u0411\u0423\u041a\u0418\u201c \u0427\u0415\u0422\u0415\u0422\u0415<\/strong> &#8211; \u0441\u0442\u0440. 530<\/p>\n<p><strong>GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u042f \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/strong> &#8211; \u0441\u0442\u0440. 532<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p><strong><a name=\"art01\"><\/a>\u0418\u041d\u0422\u0415\u0413\u0420\u0410\u0422\u0418\u0412\u041d\u0418 \u0412\u0420\u042a\u0417\u041a\u0418 \u0412 \u041a\u041e\u041c\u041f\u0415\u0422\u0415\u041d\u0422\u041d\u041e\u0421\u0422\u041d\u0418\u042f \u041f\u041e\u0414\u0425\u041e\u0414 \u0412<\/strong><strong>\u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u0418 \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0426\u0418\u041e\u041d\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418\u0418<\/strong><\/p>\n<p>\u041a\u043e\u0441\u0442\u0430 \u0413\u044a\u0440\u043e\u0432 &#8211; \u041f\u0423 \u201e\u041f\u0430\u0438\u0441\u0438\u0439 \u0425\u0438\u043b\u0435\u043d\u0434\u0430\u0440\u0441\u043a\u0438\u201c \u2013 \u041f\u043b\u043e\u0432\u0434\u0438\u0432<br \/>\u0421\u0435\u0432\u0434\u0430\u043b\u0438\u043d\u0430 \u0413\u0435\u043e\u0440\u0433\u0438\u0435\u0432\u0430, \u0415\u043b\u0435\u043d\u0430 \u041a\u043e\u0432\u0430\u0447\u0435\u0432\u0430 &#8211; \u0428\u0443\u043c\u0435\u043d\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442, \u0414\u0418\u041a\u041f\u041e \u2013 \u0412\u0430\u0440\u043d\u0430<br \/>\u0410\u043d\u0433\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432 &#8211; \u0421\u0423 \u201e\u0421\u0430\u0432\u0430 \u0414\u043e\u0431\u0440\u043e\u043f\u043b\u043e\u0434\u043d\u0438\u201c \u2013 \u0428\u0443\u043c\u0435\u043d<\/p>\n<p><strong>Abstract.<\/strong> \u0421 \u043f\u0440\u0438\u0435\u043c\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043d\u043e\u0432\u0438\u044f \u0437\u0430\u043a\u043e\u043d \u0437\u0430 \u043f\u0440\u0435\u0434\u0443\u0447\u0438\u043b\u0438\u0449\u043d\u043e \u0438 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0441\u0435 \u043f\u043e\u0441\u0442\u0430\u0432\u0438\u0445\u0430 \u043e\u0441\u043d\u043e\u0432\u0438\u0442\u0435 \u043d\u0430 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u043d\u0438\u044f \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u0431\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u043e\u0442\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435. \u0420\u0435\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0442\u043e\u0437\u0438 \u043f\u043e\u0434\u0445\u043e\u0434 \u043c\u043e\u0436\u0435 \u0434\u0430 \u0441\u0442\u0430\u043d\u0435 \u043f\u043e \u043c\u043d\u043e\u0433\u043e \u043d\u0430\u0447\u0438\u043d\u0438, \u0435\u0434\u0438\u043d \u043e\u0442 \u043a\u043e\u0438\u0442\u043e \u0435 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u0442\u0438\u0432\u043d\u0438 \u0432\u0440\u044a\u0437\u043a\u0438 \u0432 \u043f\u0440\u043e\u0446\u0435\u0441\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u043d\u043e \u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u043d\u0438\u0432\u043e. \u041d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u0435\u043d \u043c\u043e\u0434\u0435\u043b \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0441 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u0442\u0438\u0432\u043d\u0438 \u0432\u0440\u044a\u0437\u043a\u0438.<br \/><em>Keywords:<\/em> competent approach; integrative approach; model of training<\/p>\n<p>\u00a0<\/p>\n<p><strong>INTEGRATIVE<\/strong><strong>RELATIONSHIPS <\/strong><strong>I<\/strong><strong>N <\/strong><strong>T<\/strong><strong>HE COMPETENT APPROACH <\/strong><strong>I<\/strong><strong>N MATHEMATICS TECHNOLOGY TRAINING<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The adoption of the new law on preschool and school education laid the foundations for a competent approach in Bulgarian education. The implementation of this approach can be done in many ways, one of which is the implementation of integrative links in the process of training on a structural and functional level.<br \/>The present paper provides a competent model of mathematics and information technology training with integrative links.<\/p>\n<p>Prof. Dr. Kosta Garov<br \/>University of Plovdiv \u201cPaisii Hilendarski\u201d<br \/>Plovdiv, Bulgaria<\/p>\n<p>Ms. Sevdalina Georgiewa, Assist. Prof.,Dr. Elena Koleva, Assist. Prof.<br \/>Department for Information, Qualification and Continuing Education<br \/>University of Shumen<br \/>Varna, Bulgaria<\/p>\n<p>Mr. Angel Angelov<br \/>Sava Dobroplodni Secondary School<br \/>Shumen, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p><strong><a name=\"art02\"><\/a>\u041d\u042f\u041a\u041e\u0418 \u041d\u0410\u0427\u0418\u041d\u0418 \u0417\u0410 \u0420\u0415\u0428\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u0410\u041b\u0413\u0415\u0411\u0420\u0418\u0427\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><\/p>\n<p>\u00a0<\/p>\n<p style=\"text-align: left;\"><a href=\"#top\"><\/a><span style=\"font-size: 12.16px;\">Diana Stefanova<\/span><\/p>\n<p style=\"text-align: left;\">\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u0432\u0440\u044a\u0437\u043a\u0438 \u043c\u0435\u0436\u0434\u0443 \u0442\u0435\u043c\u0438\u0442\u0435 \u0432 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0438\u044f \u043a\u0443\u0440\u0441 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438.<br \/><em>Keywords<\/em>: problem solving; algebra; links between topics<\/p>\n<p>\u00a0<\/p>\n<p><strong>SOME WAYS IN SOLVING ALGEBRAIC PROBLEMS<\/strong><\/p>\n<p><strong>Abstract<\/strong>. The paper considers the possibilities of some relations among topics of the mathematical school curriculum in problem solving.<\/p>\n<p>Dr. Diana Stefanova<br \/>Asenovgrad, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p><strong><a name=\"art03\"><\/a>\u0412\u0422\u041e\u0420\u041e\u0419 \u041c\u0415\u0416\u0414\u0423\u041d\u0410\u0420\u041e\u0414\u041d\u042b\u0419 \u0421\u0415\u0422\u0415\u0412\u041e\u0419 \u0418\u0421\u0421\u041b\u0415\u0414\u041e\u0412\u0410\u0422\u0415\u041b\u042c\u0421\u041a\u0418\u0419 \u041f\u0420\u041e\u0415\u041a\u0422 \u0423\u0427\u0410\u0429\u0418\u0425\u0421\u042f \u0412 \u0420\u0410\u041c\u041a\u0410\u0425 <\/strong><strong>M<\/strong><strong>ITE<\/strong><\/p>\n<p>\u041c\u0430\u0440\u0438\u044f \u0428\u0430\u0431\u0430\u043d\u043e\u0432\u0430<br \/>\u041c\u043e\u0441\u043a\u043e\u0432\u0441\u043a\u0438\u0439 \u0438\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u043e\u0442\u043a\u0440\u044b\u0442\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u2013 \u041c\u043e\u0441\u043a\u0432\u0430 (\u0420\u043e\u0441\u0441\u0438\u044f)<br \/>\u041c\u0430\u0440\u0438\u043d\u0430 \u0411\u0435\u043b\u043e\u0440\u0443\u043a\u043e\u0432\u0430<br \/>\u041c\u0443\u043d\u0438\u0446\u0438\u043f\u0430\u043b\u044c\u043d\u043e\u0435 \u0431\u044e\u0434\u0436\u0435\u0442\u043d\u043e\u0435 \u043e\u0431\u0449\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0443\u0447\u0440\u0435\u0436\u0434\u0435\u043d\u0438\u0435 \u201e\u0421\u0440\u0435\u0434\u043d\u044f\u044f \u0448\u043a\u043e\u043b\u0430 \u2116 8\u201c \u2013 \u0410\u0440\u0445\u0430\u043d\u0433\u0435\u043b\u044c\u0441\u043a (\u0420\u043e\u0441\u0441\u0438\u044f)<br \/>\u0420\u043e\u0437\u0430 \u0410\u0442\u0430\u043c\u0443\u0440\u0430\u0442\u043e\u0432\u0430<br \/>Regional Specialized Boarding School for Gifted \nChildren with In-Depth Study of Various Subjects - Aktau, Kazakhstan<br \/>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<br \/>Technical College - Lovech<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u041e\u0434\u043d\u043e\u0439 \u0438\u0437 \u0437\u0430\u0434\u0430\u0447 \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0435\u043a\u0442\u0430 MITE (\u041c\u0435\u0442\u043e\u0434\u0438\u043a\u0438 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0438) \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e\u0437\u0434\u0430\u043d\u0438\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0439 \u0434\u043b\u044f \u0432\u044b\u044f\u0432\u043b\u0435\u043d\u0438\u044f \u0438 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u044f \u043c\u043e\u043b\u043e\u0434\u044b\u0445 \u0442\u0430\u043b\u0430\u043d\u0442\u043e\u0432. \u0421\u0440\u0435\u0434\u0438 \u0437\u0430\u0440\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u043e\u0432\u0430\u0432\u0448\u0438\u0445 \u0441\u0435\u0431\u044f \u0444\u043e\u0440\u043c \u0440\u0430\u0431\u043e\u0442\u044b \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u044b\u0439 \u043a\u043e\u043d\u043a\u0443\u0440\u0441 \u00ab\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u043f\u0440\u043e\u0435\u043a\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435\u00bb. \u041a\u043e\u043d\u043a\u0443\u0440\u0441 \u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0431\u043e\u043b\u044c\u0448\u043e\u0439 \u043f\u043e\u043f\u0443\u043b\u044f\u0440\u043d\u043e\u0441\u0442\u044c\u044e \u0441\u0440\u0435\u0434\u0438 \u0443\u0447\u0430\u0449\u0438\u0445\u0441\u044f \u0411\u043e\u043b\u0433\u0430\u0440\u0438\u0438, \u041a\u0430\u0437\u0430\u0445\u0441\u0442\u0430\u043d\u0430 \u0438 \u0420\u043e\u0441\u0441\u0438\u0438. \u0412 2017 \u0433\u043e\u0434\u0443 \u0432\u0442\u043e\u0440\u043e\u0439 \u0440\u0430\u0437 \u0432 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0443 \u043a\u043e\u043d\u043a\u0443\u0440\u0441\u0430 \u0431\u044b\u043b\u0430 \u0432\u043a\u043b\u044e\u0447\u0435\u043d\u0430 \u043d\u043e\u043c\u0438\u043d\u0430\u0446\u0438\u044f \u00ab\u0421\u0435\u0442\u0435\u0432\u044b\u0435 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u0438\u0435 \u043f\u0440\u043e\u0435\u043a\u0442\u044b\u00bb. \u041f\u0435\u0440\u0432\u043e\u0435 \u043c\u0435 \u0441\u0442\u043e \u0432 \u044d\u0442\u043e\u0439 \u043d\u043e\u043c\u0438\u043d\u0430\u0446\u0438\u0438 \u0437\u0430\u043d\u044f\u043b \u043f\u0440\u043e\u0435\u043a\u0442 \u00ab\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043c\u043e\u0437\u0430\u0438\u043a\u0430\u00bb, \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043b\u0435\u043d\u043d\u044b\u0439 \u043e\u0431\u044a\u0435\u0434\u0438\u043d\u0435\u043d\u043d\u043e\u0439 \u043a\u043e\u043c\u0430\u043d\u0434\u043e\u0439 \u0443\u0447\u0430\u0449\u0438\u0445\u0441\u044f \u0438\u0437 \u0442\u0440\u0435\u0445 \u0441\u0442\u0440\u0430\u043d: \u0411\u043e\u043b\u0433\u0430\u0440\u0438\u0439, \u041a\u0430\u0437\u0430\u0445\u0441\u0442\u0430\u043d\u0430 \u0438 \u0420\u043e\u0441\u0441\u0438\u0438. \u0414\u0430\u043d\u043d\u0430\u044f \u0441\u0442\u0430\u0442\u044c\u044f \u043f\u043e\u0434\u0432\u043e\u0434\u0438\u0442 \u0438\u0442\u043e\u0433\u0438 \u0440\u0430\u0431\u043e\u0442\u044b \u0443\u0447\u0430\u0449\u0438\u0445\u0441\u044f \u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0443 \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0430\u0446\u0438\u0438 \u0438\u0445 \u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u043e\u0439 \u0440\u0430\u0431\u043e\u0442\u044b \u043f\u043e \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0435 \u043f\u0440\u043e\u0435\u043a\u0442\u0430.<br \/><em>Keywords:<\/em> secondary education; student; geometry; research; international network collaboration; dynamical geometry software; cloud service<\/p>\n<p>\u00a0<\/p>\n<p><strong>SECOND INTERNATIONAL NET RESEARCH STUDENT PROJECT IN THE FRAMES OF MITE<\/strong><\/p>\n<p><strong>Abstract.<\/strong> One of the goals of the International project MITE (Methods and Information Technologies in education) is to create conditions for identification and development of young talents. Among the active forms with proven efficiency is the International contest \u201cMathematics and Projecting\u201d. The contest is very popular in Bulgaria, Kazakhstan and Russia. In 2017 the nomination \u201cNetwork Research Projects\u201d was included in the contest program for a second time. The project \u201cMathematical Mosaic\u201d was awarded first place in this nomination. The project was elaborated by a combined international group of students from three countries: Bulgaria, Kazakhstan and Russia. The present paper summarizes details of the students\u2019 collaboration and presents the organizational methodology in their common work during the project preparation.<\/p>\n<p>Prof. Maria Shabanova, DSc.<br \/>Moscow Institute of Open Education<br \/>125167 Moscow, Russia<\/p>\n<p>Ms. Marina Belorukova, teacher<br \/>Public Secondary School \u2116 8<br \/>163002 Arkhangelsk, Russia<\/p>\n<p>Ms. Roza Atamuratova, teacher<br \/>Regional Special Boarding School for Gifted Children with In-Deep Studying of Various Subjects<br \/>130000 Aktau, Kazakhstan<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof.<br \/>Technical College<br \/>5500 Lovech, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p><strong><a name=\"art04\"><\/a>\u0414\u0418\u0414\u0410\u041a\u0422\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0426\u0415\u041d\u0410\u0420\u0418\u0419 \u0412\u042a\u0420\u0425\u0423 \u0415\u0414\u041d\u0410 \u0417\u0410\u0414\u0410\u0427\u0410 \u041e\u0422 <\/strong><strong>XXI<\/strong><strong> \u041c\u041b\u0410\u0414\u0415\u0416\u041a\u0410 \u0411\u0410\u041b\u041a\u0410\u041d\u0421\u041a\u0410 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u0410 \u041e\u041b\u0418\u041c\u041f\u0418\u0410\u0414\u0410<\/strong><\/p>\n<p>Borislav Lazarov<br \/>Institute of Mathematics and Informatics \u2013 BAS<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0430 \u043b\u0435\u043a\u0446\u0438\u044f \u0432 \u0421\u043e\u043a\u0440\u0430\u0442\u043e\u0432 \u0441\u0442\u0438\u043b, \u0438\u0437\u043d\u0435\u0441\u0435\u043d\u0430 \u043e\u0442 \u0430\u0432\u0442\u043e\u0440\u0430 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u044f \u043c\u0430\u0439\u0441\u0442\u043e\u0440\u0441\u043a\u0438 \u043a\u043b\u0430\u0441 \u201e\u0427\u0435\u0440\u043d\u043e\u0440\u0438\u0437\u0435\u0446 \u0425\u0440\u0430\u0431\u044a\u0440\u201c, 2017 \u0433. \u041e\u0440\u0438\u0433\u0438\u043d\u0430\u043b\u043d\u0430\u0442\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 1 \u043e\u0442 XXI \u043c\u043b\u0430\u0434\u0435\u0436\u043a\u0430 \u0431\u0430\u043b\u043a\u0430\u043d\u0441\u043a\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u0435 \u0434\u0435\u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0440\u0430\u043d\u0430 \u0432 \u0441\u0435\u0440\u0438\u044f \u0441\u043f\u043e\u043c\u0430\u0433\u0430\u0442\u0435\u043b\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0430\u0442\u0430 \u0446\u0435\u043b\u0435\u0432\u0430 \u0433\u0440\u0443\u043f\u0430. \u041f\u043e \u0432\u0440\u0435\u043c\u0435 \u043d\u0430 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u043e\u0442\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0441\u0430 \u043f\u0440\u043e\u0441\u043b\u0435\u0434\u0435\u043d\u0438 \u0434\u0432\u0430 \u0438\u043d\u0434\u0438\u043a\u0430\u0442\u043e\u0440\u0430 \u0437\u0430 \u043f\u0440\u043e\u0433\u0440\u0435\u0441. \u041d\u0430\u043f\u0440\u0430\u0432\u0435\u043d\u0438\u0442\u0435 \u043f\u0440\u0435\u0434\u0432\u0430\u0440\u0438\u0442\u0435\u043b\u043d\u0438 \u0438\u0437\u0432\u043e\u0434\u0438 \u0431\u0438\u0445\u0430 \u043c\u043e\u0433\u043b\u0438 \u0434\u0430 \u0431\u044a\u0434\u0430\u0442 \u043f\u043e\u043b\u0435\u0437\u043d\u0438 \u043f\u0440\u0438 \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430\u0442\u0430 \u043d\u0430 \u0438\u0437\u044f\u0432\u0435\u043d\u0438 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u0430 \u043a\u044a\u043c \u0432\u043d\u0435\u0434\u0440\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0438\u0437\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u0441\u043a\u0438 \u043f\u043e\u0434\u0445\u043e\u0434.<br \/><em>Keywords:<\/em> inquiry-based approach; problem decomposition; Socratic style teaching<\/p>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong>DIDACTIC SCENARIO ON A PROBLEM FROM THE 21<sup>ST<\/sup> JUNIOR BALKAN MATHEMATICAL OLYMPIAD<\/strong><\/p>\n<p><strong>Abstract<\/strong>. The paper presents a lecture in Socratic style given by the author during the Chernorizec Hrabar Math Master Class, 2017. The genuine Problem 1 from the competition paper of the 21stJunior Balkan Math Olympiad has been decomposed in series of auxiliary problems with respect to a particular target group. Two indicators for progress have been observed during the experiment, both related to the inquiry-based teaching. The conclusions drawn could be potentially helpful in training advanced students in mathematics via the inquiry-based method.<\/p>\n<p>Prof. Dr. Borislav Lazarov<br \/>Institute of Mathematics and Informatics<br \/>Bulgarian Academy of Sciences<br \/>1113 Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u00a0\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p><strong><a name=\"art05\"><\/a>SOME NUMERICAL SEQUENCES CONCERNING SQUARE ROOTS (PART ONE<\/strong><strong>)<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract<\/strong>. The article is dedicated to one type of problems with an infinite number of nested square radicals proposed in mathematical competitions. A generalization is considered and the deduced theoretical relation is proved by the method of the complete mathematical induction.<br \/><em>Keywords<\/em>: infinite sequence; nested radical; convergence; mathematical induction.<\/p>\n<p>Dr. Rosen Nikolaev, Assoc. Prof., Dr. Tanka Milkova, Assoc. Prof., Dr. Jordan Petkov, Assist. Prof.<br \/>University of Economics \u2013 Varna<br \/>9002 Varna, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p><strong><a name=\"art06\"><\/a>\u0414\u041e\u041a\u0410\u0417\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u0410 \u0418 \u0423\u0422\u041e\u0427\u041d\u0415\u041d\u0418\u042f \u041d\u0410 \u0415\u041a\u0421\u041f\u0415\u0420\u0418\u041c\u0415\u041d\u0422\u0410\u041b\u041d\u041e \u041f\u041e\u041b\u0423\u0427\u0415\u041d\u0418\u0422\u0415 \u0422\u0412\u042a\u0420\u0414\u0415\u041d\u0418\u042f \u0427\u0420\u0415\u0417 \u041f\u0420\u0418\u041d\u0426\u0418\u041f\u0410 \u0417\u0410 \u0414\u0423\u0410\u041b\u041d\u041e\u0421\u0422<\/strong><\/p>\n<p>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0438\u0441\u0448\u0435 \u0443\u0447\u0438\u043b\u0438\u0449\u0435 \u043f\u043e \u0437\u0430\u0441\u0442\u0440\u0430\u0445\u043e\u0432\u0430\u043d\u0435 \u0438 \u0444\u0438\u043d\u0430\u043d\u0441\u0438 \u2013 \u0421\u043e\u0444\u0438\u044f<br \/>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432, \u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u041b\u043e\u0432\u0435\u0447<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0430 \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u0442\u0430, \u043a\u043e\u0438\u0442\u043e \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0437\u0438\u0440\u0430\u0442 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438\u0442\u0435 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438, \u043e\u043f\u0438\u0441\u0430\u043d\u0438 \u0432 (Grozdev &amp; Nenkov, 2017). \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438\u0442\u0435 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430 \u0432\u043e\u0434\u044f\u0442 \u0434\u043e \u0443\u0442\u043e\u0447\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043e\u0442 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u0442\u0430, \u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0430\u043d\u0438 \u0432 (Grozdev &amp; Nenkov, 2017).<br \/><em>Keywords:<\/em> triangle; centroid; circumcurve; Euler curve; Euler line<\/p>\n<p>\u00a0<\/p>\n<p><strong>PROOFS AND SPECIFICATIONS OF EXPERIMENTALLY DERIVED ASSERTIONS BY THE DUALITY PRINCIPLE<\/strong><\/p>\n<p><strong>Abstract<\/strong>. Properties are proved in the paper, which characterize the geometric constructions described in (Grozdev &amp; Nenkov, 2017). The proposed proofs lead to specifications of some of the properties formulated in (Grozdev &amp; Nenkov, 2017).<\/p>\n<p>Prof. Sava Grozdev, DSc<br \/>University of Finance, Business and Entrepreneurship<br \/>1618 Sofia, Bulgaria<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof.<br \/>Technical College<br \/>5500 Lovech, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p class=\"StyleBIEmailAddress95pt\"><strong><a name=\"art07\"><\/a>ERD\u00d6S\u2019 DISTINCT DISTANCES PROBLEM<\/strong><\/p>\n<p class=\"StyleBIEmailAddress95pt\">\u00a0<\/p>\n<p><strong>Abstract.<\/strong> In discrete geometry, the Erd\u00f6s\u2019 distinct distances problem states that between n distinct points in a plane there are at least distinct distances. The problem was posed by Paul Erd\u00f6s in 1946. In 2010, Larry Guth and Net Hawk Katz claimed to have a solution. The solution was published in 2015 in the Annals of Mathematics. This article aims at popularizing this problem to young students in mathematics, therefore no big background in mathematics is needed to understand it. It is open to every reader and shall be improved with any remarks or questions.<br \/><em>Keywords:<\/em> geometry; the Erd\u00f6s\u2019 distinct distances problem; young students<\/p>\n<p>Mr. Houssam Zenati<br \/>Centrale Supelec (Ecole Centrale)<br \/>France<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u00a0\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>\n<p class=\"PaperTitle\" align=\"left\"><strong><span lang=\"EN-US\"><a name=\"art08\"><\/a>OPTIMIZING THE POSITIONING OF SERVING UNITS IN THE TOURISM BUSINESS<\/span><\/strong><\/p>\n<p class=\"PaperTitle\" align=\"left\">\u00a0<\/p>\n<p><span style=\"font-size: 12.16px;\"><strong>Abstract.<\/strong> In the present paper an idea for optimizing the positioning of serving units in tourism business is revealed using some applications of mathematics in economics. The elaboration has a methodological character. Methodologically the authors assume that some tourist objects (hotels, restaurants, etc.) are given and they try to determine the best possible position for a serving unit (store, office, etc.) using a set of optimization problems. Finally, an approbation of the results with a real example is considered.<\/span><\/p>\n<p><em>Keywords:<\/em> optimization; tourism; serving unit; positioning<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Radan Miryanov, Assist. Prof., Dr. Velina Yordanova, Assist. Prof.<br \/>University of Economics \u2013 Varna<br \/>Varna, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>","protected":false},"excerpt":{"rendered":"<p>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u00a0 EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418\u0418\u043d\u0442\u0435\u0433\u0440\u0430\u0442\u0438\u0432\u043d\u0438 \u0432\u0440\u044a\u0437\u043a\u0438 \u0432 \u043a\u043e\u043c\u043f\u0435\u0442\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u043d\u0438\u044f \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438\u0438 [Information Integrative Relationships in the Competent Approach in Mathematics Technology Training] \/ \u041a\u043e\u0441\u0442\u0430 \u0413\u044a\u0440\u043e\u0432, \u0421\u0435\u0432\u0434\u0430\u043b\u0438\u043d\u0430 \u0413\u0435\u043e\u0440\u0433\u0438\u0435\u0432\u0430, \u0415\u043b\u0435\u043d\u0430 \u041a\u043e\u0432\u0430\u0447\u0435\u0432\u0430, \u0410\u043d\u0433\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432 \/ Kosta Garov, Sevdalina Georgieva, Elena Kovacheva, Angel Angelov &#8211; \u0441\u0442\u0440. 439 \u041d\u044f\u043a\u043e\u0438 \u043d\u0430\u0447\u0438\u043d\u0438 \u0437\u0430 [&hellip;]<\/p>","protected":false},"author":1,"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":[3486],"tags":[],"yoast_head":"<!-- This site is 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