{"id":40639,"date":"2016-02-07T21:59:00","date_gmt":"2016-02-07T18:59:00","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016\/mathinfocontent012016\/"},"modified":"2019-06-18T21:58:29","modified_gmt":"2019-06-18T18:58:29","slug":"mathinfocontent012016","status":"publish","type":"post","link":"https:\/\/press.azbuki.bg\/en\/matematics\/matharticles2016\/mathinfocontent012016\/","title":{"rendered":"Mathematics and Informatics, Number 1\/2016, Volume 59"},"content":{"rendered":"<p><strong><a name=\"top\"><br \/> <\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 <\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDITORIAL \/ \u041a\u042a\u041c \u0427\u0418\u0422\u0410\u0422\u0415\u041b\u042f<\/strong> &ndash; \u0441\u0442\u0440. 7<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/03\/azbuki.bg_dmdocuments_Matematika_012016_Obrashtenie.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL MATTERS \/ \u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e <\/strong><\/p>\n<p><a href=\"#art01\"> \u0410\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u0435\u043d \u0438\u043b\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u0435\u043d \u043c\u0435\u0442\u043e\u0434 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0430\u0442\u0430 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 <br \/>[Arithmetical or Algebraic Method in Solving Primary School Mathematical Problems] <\/a>\/ <br \/>\u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, \u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430, \u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430 \/ Zdravko Lalchev, Margarita Varbanova, Irina Voutova &ndash; \u0441\u0442\u0440. 11<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/03\/azbuki.bg_dmdocuments_Matematika_012016_Zdravko-Lalchev_i_avtori.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art02\"> \u0420\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0434\u0438\u0434\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0435\u0439 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u0438 \u043a\u043e\u043c\u043c\u0443\u043d\u0438\u043a\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0439 <br \/>\u0432 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0438 \u0442\u0432\u043e\u0440\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u043f\u043e\u0441\u043e\u0431\u043d\u043e\u0441\u0442\u0435\u0439 \u0438 \u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u0438\u0445 \u043d\u0430\u0432\u044b\u043a\u043e\u0432<br \/> [Realization of the Didactic Possibilities of the Information and Communication Technologies <br \/>in the Formation of Creative Skills and The Development of Investigating Habits] <\/a>\/<br \/> \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u0420\u0443\u0441\u0430\u043a\u043e\u0432 \/ Alexander Rusakov &ndash; \u0441\u0442\u0440. 29<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/03\/azbuki.bg_dmdocuments_Matematika_012016_Alexander-Rusakov.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL RESEARCH \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418<\/strong><\/p>\n<p><a href=\"#art03\"> Stationary Numbers <\/a>\/ Smaiyl Makyshov &ndash; \u0441\u0442\u0440. 43<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/03\/azbuki.bg_dmdocuments_Matematika_012016_Smaiyl-Makyshov.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art04\"> \u041e\u0431\u0449 \u043f\u043e\u0434\u0445\u043e\u0434 \u0437\u0430 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043c\u0435\u0436\u0434\u0443 \u0440\u0430\u0434\u0438\u0443\u0441\u0438 \u043d\u0430 \u0434\u043e\u043f\u0438\u0440\u0430\u0449\u0438 \u0441\u0435 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438 <br \/>[A General Approach to Establish Relations Among The Radii of Tangent Circles] <\/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 &ndash; \u0441\u0442\u0440. 52<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/03\/azbuki.bg_dmdocuments_Matematika_012016_Sava-Grozdev_Veselin-Nenkov.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art05\">\u0418\u0437\u0432\u044a\u043d\u043a\u043b\u0430\u0441\u043d\u0438\u0442\u0435 \u0434\u0435\u0439\u043d\u043e\u0441\u0442\u0438 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 &ndash; \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0430\u0442\u0430 \u0444\u043e\u0440\u043c\u0430 \u0437\u0430 \u043c\u043e\u0442\u0438\u0432\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 <br \/>[Extracurricular Activities in Mathematics &ndash; a Different Form for Student Motivation] <\/a>\/ <br \/>\u0417\u0430\u0440\u0430 \u0414\u0430\u043d\u0430\u0438\u043b\u043e\u0432\u0430-\u0421\u0442\u043e\u0439\u043d\u043e\u0432\u0430, \u0418\u0432\u0430\u0439\u043b\u043e \u0421\u0442\u0430\u0440\u0438\u0431\u0440\u0430\u0442\u043e\u0432 \/ Zara Danailova-Stoynova, Ivaylo Staribratov &ndash; \u0441\u0442\u0440. 73<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/03\/azbuki.bg_dmdocuments_Matematika_012016_Zara-Danailova-Stoynova_Ivaylo-Staribratov.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>OLYMPIADS. COMPETITIONS \/ \u041e\u041b\u0418\u041c\u041f\u0418\u0410\u0414\u0418. \u0421\u042a\u0421\u0422\u0415\u0417\u0410\u041d\u0418\u042f<\/strong><\/p>\n<p><a href=\"#art06\">\u0422\u0440\u0438\u043d\u0430\u0434\u0435\u0441\u0435\u0442\u0430 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u043a\u0430 <br \/>[Thirteenth International Linguistics Olympiad] <\/a>\/ <br \/>\u0418\u0432\u0430\u043d \u0414\u0435\u0440\u0436\u0430\u043d\u0441\u043a\u0438 \/ Ivan Derzhanski &ndash; \u0441\u0442\u0440. 83<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/03\/azbuki.bg_dmdocuments_Matematika_012016_Ivan-Derzhanski.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art07\"> \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u0416\u0430\u0443\u0442\u0438\u043a\u043e\u0432\u0441\u043a\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434a<br \/> [International Zhautikov Olympiad] <\/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 &ndash; \u0441\u0442\u0440. 89<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/03\/azbuki.bg_dmdocuments_Matematika_012016_Sava-Grozdev_Veselin-Nenkov_2.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>CONTEST PROBLEMS \/ \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><\/p>\n<p>Contest Problems of this Issue<br \/> [Contest Problems of the Issue] &ndash; \u0441\u0442\u0440. 95<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/03\/azbuki.bg_dmdocuments_Matematika_012016_Zadachi-na-broy.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u043a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u0431\u0440\u043e\u0439 6, 2015 <br \/>[Solutions of the Contest Problems from issue 6, 2015] &ndash; \u0441\u0442\u0440. 97<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/03\/azbuki.bg_dmdocuments_Matematika_012016_Reshenie-na-zadachi-ot-broy-2_2015.pdf\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>READ IN THE LATEST ISSUES OF &bdquo;AZ BUKI&ldquo; JOURNALS \/ <br \/>\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 &bdquo;\u0410\u0417 \u0411\u0423\u041a\u0418&ldquo; \u0427\u0415\u0422\u0415\u0422\u0415<\/strong> &ndash; \u0441\u0442\u0440. 99<\/p>\n<p>&nbsp;<\/p>\n<p><strong>GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/strong> &ndash; \u0441\u0442\u0440. 100<\/p>\n<p><strong><strong>&nbsp;<\/strong><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"atr01\"><\/a> \u0410\u0420\u0418\u0422\u041c\u0415\u0422\u0418\u0427\u0415\u041d \u0418\u041b\u0418 \u0410\u041b\u0413\u0415\u0411\u0420\u0418\u0427\u0415\u041d \u041c\u0415\u0422\u041e\u0414 \u041f\u0420\u0418 \u0420\u0415\u0428\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u0417\u0410\u0414\u0410\u0427\u0418 \u0412 \u041d\u0410\u0427\u0410\u041b\u041d\u0410\u0422\u0410 \u0423\u0427\u0418\u041b\u0418\u0429\u041d\u0410 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Zdravko Lalchev, Irina Voutova<\/strong><\/p>\n<p>\u0421\u043e\u0444\u0438\u0439\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 &bdquo;\u0421\u0432. \u041a\u043b\u0438\u043c\u0435\u043d\u0442 \u041e\u0445\u0440\u0438\u0434\u0441\u043a\u0438&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430<\/strong><\/p>\n<p>\u0412\u0435\u043b\u0438\u043a\u043e\u0442\u044a\u0440\u043d\u043e\u0432\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 &bdquo;\u0421\u0432. \u0441\u0432. \u041a\u0438\u0440\u0438\u043b \u0438 \u041c\u0435\u0442\u043e\u0434\u0438\u0439&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> \u0426\u0435\u043b\u0442\u0430 \u043d\u0430 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u0434\u0430 \u043e\u0447\u0435\u0440\u0442\u0430\u0435 \u0433\u0440\u0430\u043d\u0438\u0446\u0438\u0442\u0435 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0442\u043e &bdquo;\u043f\u043e\u043a\u0440\u0438\u0442\u0438\u0435&ldquo; \u043d\u0430 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438\u0442\u0435 \u043c\u0435\u0442\u043e\u0434\u0438 \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u043d\u0430\u0447\u0430\u043b\u043d\u0438\u044f \u043a\u0443\u0440\u0441 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0434\u0430 \u043e\u0442\u0433\u043e\u0432\u043e\u0440\u0438 \u043d\u0430 \u0432\u044a\u043f\u0440\u043e\u0441\u0430 \u0432 \u043a\u043e\u0438 \u0441\u043b\u0443\u0447\u0430\u0438 \u043c\u043e\u0434\u0435\u043b\u0438\u0442\u0435 \u043d\u0430 \u043a\u043b\u0430\u0441\u0438\u0447\u0435\u0441\u043a\u0430\u0442\u0430 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430 \u043d\u0430 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430\u0442\u0430 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u043a\u0430 \u0441\u0430 &bdquo;\u0431\u0435\u0437\u0441\u0438\u043b\u043d\u0438&ldquo; \u0438 \u043f\u043e \u0442\u0430\u0437\u0438 \u043f\u0440\u0438\u0447\u0438\u043d\u0430 \u0435 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0434\u0430 \u0441\u0435 \u043f\u043e\u0442\u044a\u0440\u0441\u0438 &bdquo;\u043f\u043e\u043c\u043e\u0449&ldquo; \u043e\u0442 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430\u0442\u0430 \u043d\u0430 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430\u0442\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0430. \u041a\u0430\u0437\u0430\u043d\u043e \u043f\u043e \u0434\u0440\u0443\u0433 \u043d\u0430\u0447\u0438\u043d, \u0446\u0435\u043b\u0442\u0430 \u0435 \u0434\u0430 \u0441\u0435 \u043f\u043e\u043a\u0430\u0436\u0435 \u043a\u043e\u0433\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u043d\u0438\u044f\u0442 \u043f\u043e\u0434\u0445\u043e\u0434 \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0435 \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438 \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u0435\u043d \u0438\u043b\u0438 \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u043d. \u041d\u0430 \u043e\u0441\u043d\u043e\u0432\u0430\u0442\u0430 \u043d\u0430 MZ-\u043a\u0430\u0440\u0442\u0430\u0442\u0430 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430\u0442\u0430 \u0430\u0432\u0442\u043e\u0440\u0438\u0442\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0430\u0442 \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0439 \u0437\u0430 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442 \u043e\u0442 \u0432\u044a\u0432\u0435\u0436\u0434\u0430\u043d\u0435 \u043d\u0430 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e \u0438 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043c\u043e\u0434\u0435\u043b \u043e\u0442 \u0441\u044a\u0441\u0442\u0430\u0432\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u043d\u0430\u0447\u0430\u043b\u043d\u0430\u0442\u0430 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430.<\/p>\n<p>Keywords: MZ-card, inversion, equation, algebraic method, mathematical model, arithmetical knot<\/p>\n<p>&nbsp;<\/p>\n<p><strong>ARITHMETICAL OR ALGEBRAIC METHOD IN SOLVING PRIMARY SCHOOL MATHEMATICAL PROBLEMS <\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> The purpose of the present paper is to outline the boundaries of the mathematical &bdquo;cover&ldquo; of the arithmetical approaches in solving primary course mathematical problems. The paper studies the cases when classical didactic models of school arithmetics are &bdquo;helpless&ldquo; and provoke searching of &bdquo;help&ldquo; from school algebra didactics. In other words, the purpose is to show when the algebraic approach is logically unavoidable or technically excusable in solving primary school arithmetical problems. On the basis of the MZ-card of the problem the authors formulate a criterion for the necessity of introducing an unknown variable and applying a mathematical model of compound equations in solving primary school mathematical problems.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\uf02aProf. Zdravko Lalchev, PhD<\/strong><\/p>\n<p>Faculty of Preschool and Primary Education<\/p>\n<p>University of Sofia<\/p>\n<p>69A, Shipchenski prohod Blvd.<\/p>\n<p>1574 Sofia, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\uf02aProf. Margarita Varbanova, PhD<\/strong><\/p>\n<p>Faculty of Mathematics and Informatics<\/p>\n<p>University of VelikoTarnovo<\/p>\n<p>3A, Arh. G. Kozarev Blvd.<\/p>\n<p>5000 Veliko Tarnovo, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p>\uf02a<strong>Dr. Irina Voutova, Assist. Prof<\/strong><\/p>\n<p>Faculty of Mathematics and Informatics<\/p>\n<p>University of Sofia<\/p>\n<p>5, James Boucher Blvd.<\/p>\n<p>1164 Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"atr02\"><\/a> \u0420\u0415\u0410\u041b\u0418\u0417\u0410\u0426\u0418\u042f \u0414\u0418\u0414\u0410\u041a\u0422\u0418\u0427\u0415\u0421\u041a\u0418\u0425 \u0412\u041e\u0417\u041c\u041e\u0416\u041d\u041e\u0421\u0422\u0415\u0419 \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0426\u0418\u041e\u041d\u041d\u042b\u0425 \u0418 \u041a\u041e\u041c\u041c\u0423\u041d\u0418\u041a\u0410\u0426\u0418\u041e\u041d\u041d\u042b\u0425 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0419 \u0412 \u0420\u0410\u0417\u0412\u0418\u0422\u0418\u0418 \u0422\u0412\u041e\u0420\u0427\u0415\u0421\u041a\u0418\u0425 \u0421\u041f\u041e\u0421\u041e\u0411\u041d\u041e\u0421\u0422\u0415\u0419 \u0418 \u0424\u041e\u0420\u041c\u0418\u0420\u041e\u0412\u0410\u041d\u0418\u0418 \u0418\u0421\u0421\u041b\u0415\u0414\u041e\u0412\u0410\u0422\u0415\u041b\u042c\u0421\u041a\u0418\u0425 \u041d\u0410\u0412\u042b\u041a\u041e\u0412<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u0420\u0443\u0441\u0430\u043a\u043e\u0432<\/strong><\/p>\n<p>\u041c\u043e\u0441\u043a\u043e\u0432\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0440\u0430\u0434\u0438\u043e\u0442\u0435\u0445\u043d\u0438\u043a\u0438, \u044d\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u0438\u043a\u0438 \u0438 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u043a\u0438<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u0445 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u0440\u0430\u0441\u043a\u0440\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0434\u0438\u0434\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u0438 \u043a\u043e\u043c\u043c\u0443\u043d\u0438\u043a\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0439 (\u0418\u041a\u0422), \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0438\u0445 &bdquo;\u043f\u043e\u0434\u0442\u043e\u043b\u043a\u043d\u0443\u0442\u044c&ldquo; \u0443\u0447\u0430\u0449\u0435\u0433\u043e\u0441\u044f \u043a \u043e\u0442\u043a\u0440\u044b\u0442\u0438\u044e \u0441\u0443\u0431\u044a\u0435\u043a\u0442\u0438\u0432\u043d\u043e \u043d\u043e\u0432\u044b\u0445 \u0437\u043d\u0430\u043d\u0438\u0439, \u0430 \u0438\u043d\u043e\u0433\u0434\u0430 \u0438 \u043e\u0431\u044a\u0435\u043a\u0442\u0438\u0432\u043d\u043e \u043d\u043e\u0432\u044b\u0445 \u0432 \u043d\u0430\u0443\u043a\u0435 \u0444\u0430\u043a\u0442\u043e\u0432.<\/p>\n<p>Keywords: Didactics, ICT technologies, computer environment, visualization, creativity<\/p>\n<p>&nbsp;<\/p>\n<p><strong>REALIZATION OF THE DIDACTIC POSSIBILITIES OF THE INFORMATION AND COMMUNICATION TECHNOLOGIES IN THE FORMATION OF CREATIVE SKILLS AND THE DEVELOPMENT OF INVESTIGATING HABITS<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> On examples of specific problems the paper reveals some didactic possibilities of the Information and Communication Technologies (ICT) in order to &ldquo;push&rdquo; students to discover subjective new knowledge and sometimes objectively new scientific facts.<\/p>\n<p>\uf02aProf. Alexander Rusakov, DSc<\/p>\n<p>Moscow State Technical University<\/p>\n<p>of Radioengineering, Electronics and Automation<\/p>\n<p>Moscow, Russia<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"atr03\"><\/a>STATIONARY NUMBERS<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Smaiyl Makyshov<\/strong><\/p>\n<p>Haileybury Almaty School<\/p>\n<p>Abstract. The article studies one method of numbers generation. For this new method we define and study sets of so called m-digitaddition and m-self positive integers. In addition, we introduce a stationary number term for the mentioned operation and provide a full description of the set of stationary numbers under some conditions.<\/p>\n<p>Keywords: Kaprekar, generator, digitaddition, self number.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Mr. Smaiyl Makyshov<\/strong><\/p>\n<p>Haileybury Almaty School&nbsp;&nbsp;<\/p>\n<p>Almaty, Kazakhstan<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"atr04\"><\/a>\u041e\u0411\u0429 \u041f\u041e\u0414\u0425\u041e\u0414 \u0417\u0410 \u0423\u0421\u0422\u0410\u041d\u041e\u0412\u042f\u0412\u0410\u041d\u0415 \u041d\u0410 \u0417\u0410\u0412\u0418\u0421\u0418\u041c\u041e\u0421\u0422\u0418 \u041c\u0415\u0416\u0414\u0423 \u0420\u0410\u0414\u0418\u0423\u0421\u0418 \u041d\u0410 \u0414\u041e\u041f\u0418\u0420\u0410\u0429\u0418 \u0421\u0415 \u041e\u041a\u0420\u042a\u0416\u041d\u041e\u0421\u0422\u0418<\/strong><\/p>\n<p><strong><br \/>Sava Grozdev<\/strong>, \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<\/p>\n<p><strong><br \/>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<\/strong>, \u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 &ndash; \u041b\u043e\u0432\u0435\u0447<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0430 \u0435 \u0435\u0434\u043d\u0430 \u043e\u0431\u0449\u0430 \u0438\u0434\u0435\u044f \u0437\u0430 \u043d\u0430\u043c\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043c\u0435\u0436\u0434\u0443 \u0440\u0430\u0434\u0438\u0443\u0441\u0438\u0442\u0435 \u043d\u0430 \u0434\u043e\u043f\u0438\u0440\u0430\u0449\u0438 \u0441\u0435 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438 \u0432 \u0440\u0430\u0432\u043d\u0438\u043d\u0430\u0442\u0430 \u043d\u0430 \u0434\u0430\u0434\u0435\u043d \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a.&nbsp;\u0412 \u043e\u0441\u043d\u043e\u0432\u0430\u0442\u0430 \u0441\u0438 \u0442\u0430\u0437\u0438 \u0438\u0434\u0435\u044f \u0441\u044a\u0434\u044a\u0440\u0436\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0442\u0430 \u043d\u0430 \u041e\u0439\u043b\u0435\u0440 \u0437\u0430 \u0440\u0430\u0437\u0441\u0442\u043e\u044f\u043d\u0438\u0435\u0442\u043e \u043c\u0435\u0436\u0434\u0443 \u0446\u0435\u043d\u0442\u0440\u043e\u0432\u0435\u0442\u0435 \u043d\u0430 \u043e\u043f\u0438\u0441\u0430\u043d\u0430\u0442\u0430 \u0438 \u0432\u043f\u0438\u0441\u0430\u043d\u0430\u0442\u0430 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 \u0438 \u0434\u0440\u0443\u0433\u0438 \u0432\u0440\u044a\u0437\u043a\u0438 \u043c\u0435\u0436\u0434\u0443 \u0440\u0430\u0434\u0438\u0443\u0441\u0438\u0442\u0435 \u043d\u0430 \u0442\u0435\u0437\u0438 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438. \u041e\u0441\u043d\u043e\u0432\u043d\u0438\u0442\u0435 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438 \u0441\u0430 \u043e\u0431\u0435\u0434\u0438\u043d\u0435\u043d\u0438 \u0432\u044a\u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u043a\u0430\u0442\u0430 \u0438 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e\u0442\u043e \u043d\u0430 \u0441\u044a\u043e\u0442\u0432\u0435\u0442\u043d\u0430 \u043b\u0435\u043c\u0430.<\/p>\n<p>Keywords: triangle, circle, circum-circle, in-circle, Sangaku<\/p>\n<p>&nbsp;<\/p>\n<p><strong>A GENERAL APPROACH TO ESTABLISH RELATIONS AMONG THE RADII OF TANGENT CIRCLES <\/strong><\/p>\n<p><strong>Abstract.<\/strong> A general idea is considered to establish relations among the radii of tangent circles in the plane of a given triangle. The idea is based on Euler&rsquo;s formula for the distance between the radii of the circum-circle and the in-circle of the triangle and also on some other relations between the radii in question. The main results are unified in the formulation of a corresponding lemma.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\uf02aProf. Sava Grozdev, DSc<\/strong><\/p>\n<p>University of Finance, Business and Entrepreneurship<\/p>\n<p>1, Gusla Str.<\/p>\n<p>1618 Sofia, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\uf02aDr. Veselin Nenkov, Assoc. Prof.<\/strong><\/p>\n<p>Technical College Lovech<\/p>\n<p>31, Sajko Saev Str.<\/p>\n<p>Lovech, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"atr05\"><\/a>\u0418\u0417\u0412\u042a\u041d\u041a\u041b\u0410\u0421\u041d\u0418\u0422\u0415 \u0414\u0415\u0419\u041d\u041e\u0421\u0422\u0418 \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 &ndash; \u0420\u0410\u0417\u041b\u0418\u0427\u041d\u0410\u0422\u0410 \u0424\u041e\u0420\u041c\u0410 \u0417\u0410 \u041c\u041e\u0422\u0418\u0412\u0418\u0420\u0410\u041d\u0415 \u041d\u0410 \u0423\u0427\u0415\u041d\u0418\u0426\u0418\u0422\u0415<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u0417\u0430\u0440\u0430 \u0414\u0430\u043d\u0430\u0438\u043b\u043e\u0432\u0430-\u0421\u0442\u043e\u0439\u043d\u043e\u0432\u0430<\/strong>, \u0420\u0418\u041e &ndash; \u041f\u043b\u043e\u0432\u0434\u0438\u0432<\/p>\n<p><strong>Ivailo Staribratov<\/strong>, \u041f\u043b\u043e\u0432\u0434\u0438\u0432\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0441\u043c\u0435 \u0441\u043f\u043e\u0434\u0435\u043b\u0438\u043b\u0438 \u0441\u0432\u043e\u044f \u043e\u043f\u0438\u0442 \u043f\u0440\u0438 \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0438\u0437\u0432\u044a\u043d\u043a\u043b\u0430\u0441\u043d\u0438 \u0444\u043e\u0440\u043c\u0438 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0438 \u043d\u0430 \u0438\u0437\u044f\u0432\u0438 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u043e\u0442 \u043f\u0435\u0442\u0438 \u0434\u043e \u0441\u0435\u0434\u043c\u0438 \u043a\u043b\u0430\u0441. \u0421 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u0430\u043d\u043a\u0435\u0442\u0430 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u0445\u043c\u0435 \u043a\u043e\u0438 \u0441\u0430 \u043f\u0440\u0438\u0447\u0438\u043d\u0438\u0442\u0435 \u0437\u0430 \u0432\u043a\u043b\u044e\u0447\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0432 \u0442\u0430\u043a\u0438\u0432\u0430 \u0444\u043e\u0440\u043c\u0438, \u043a\u0430\u043a\u0432\u0438 \u0441\u0430 \u0442\u0435\u0445\u043d\u0438\u0442\u0435 \u043c\u043e\u0442\u0438\u0432\u0438 \u0437\u0430 \u0437\u0430\u0434\u044a\u043b\u0431\u043e\u0447\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u043d\u0430\u043d\u0438\u044f\u0442\u0430 \u0438 \u043e\u0442 \u043a\u0430\u043a\u0432\u043e \u0441\u0430 \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u0436\u0435\u043b\u0430\u043d\u0438\u044f\u0442\u0430 \u0438\u043c \u0437\u0430 \u0438\u0437\u044f\u0432\u0430.<\/p>\n<p>Keywords: extracurricular activities, research, motivation, striving for expression<\/p>\n<p>&nbsp;<\/p>\n<p><strong>EXTRACURRICULAR ACTIVITIES IN MATHEMATICS &ndash; A DIFFERENT FORM FOR STUDENT MOTIVATION<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> In the present paper we have shared our experience in the organization of extracurricular training activities and performances in mathematics of students from fifth to seventh grade. Using an inquiry we have studied the reasons for the participation of students in such forms, what is the motivation to deep their knowledge and what initiates their striving to express themselves.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\uf02aMrs. Zara Danailova-Stoynova<\/strong><\/p>\n<p>Senior expert in Mathematics<\/p>\n<p>Regional Inspectorate of Education<\/p>\n<p>Plovdiv, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\uf02aDr. Ivaylo Staribratov, Assoc. Prof.<\/strong><\/p>\n<p>Plovdiv University<\/p>\n<p>Plovdiv, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"atr06\"><\/a>\u0422\u0420\u0418\u041d\u0410\u0414\u0415\u0421\u0415\u0422\u0410 \u041c\u0415\u0416\u0414\u0443\u041d\u0410\u0420\u041e\u0414\u041d\u0410 \u041e\u041b\u0418\u041c\u041f\u0418\u0410\u0414\u0410 \u041f\u041e \u041b\u0418\u041d\u0413\u0412\u0418\u0421\u0422\u0418\u041a\u0410<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Ivan Derzhanski<\/strong>, \u0418\u0441\u0442\u0438\u0442\u0443\u0442 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 &ndash; \u0411\u0410\u041d<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u0430\u0442\u0430 \u043f\u0440\u0435\u0437 2015 \u0433. \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u043a\u0430. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0441\u0430 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u043d\u0430 \u0431\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u0438\u0442\u0435 \u0443\u0447\u0430\u0441\u0442\u043d\u0438\u0446\u0438, \u0447\u0430\u0441\u0442 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u0438 \u0442\u0435\u0445\u043d\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f.<\/p>\n<p>Keywords: linguistics, Olympiad, problem solution.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>THIRTEENTH INTERNATIONAL LINGUISTICS OLYMPIAD<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The paper is dedicated to the International Linguistics Olympiad in 2015. What are presented are the results of the Bulgarian participants, some of the tasks and their solutions.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\uf02aDr. Ivan Derzhanski, Assoc. Prof.<\/strong><\/p>\n<p>Institute of Mathematics and Informatics<\/p>\n<p>Acad. G. Bonchev Str., block 8<\/p>\n<p>1113 Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a name=\"atr07\"><\/a> \u041c\u0415\u0416\u0414\u0423\u041d\u0410\u0420\u041e\u0414\u041d\u0410 \u0416\u0410\u0423\u0422\u0418\u041a\u041e\u0412\u0421\u041a\u0410 \u041e\u041b\u0418\u041c\u041f\u0418\u0410\u0414\u0410<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Sava Grozdev<\/strong>, \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<\/p>\n<p><strong>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<\/strong>, \u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 &ndash; \u041b\u043e\u0432\u0435\u0447<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0441\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u0438 \u0442\u0435\u0445\u043d\u0438\u0442\u0435 \u0440\u0435\u0448\u0435\u043d\u0438 \u043e\u0442 \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430\u0442\u0430 \u0416\u0430\u0443\u0442\u0438\u043a\u043e\u0432\u0441\u043a\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u0440\u0435\u0437 2016 \u0433. \u0420\u0435\u0448\u0435\u043d\u0438\u044f\u0442\u0430 \u0438\u043c\u0430\u0442 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>INTERNATIONAL ZHAUTIKOV OLYMPIAD <\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract.<\/strong> The problems of the International Zhautikov Olympiad in 2016 and their solutions are considered. Methodological&nbsp; solutions are proposed.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Prof. Sava Grozdev, DSc<\/strong><\/p>\n<p>University of Finance, Business and Entrepreneurship<\/p>\n<p>1, Gusla Str.<\/p>\n<p>1618 Sofia, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\uf02aDr. Veselin Nenkov, Assoc. Prof.<\/strong><\/p>\n<p>Technical College Lovech<\/p>\n<p>31, Sajko Saev Str.<\/p>\n<p>Lovech, Bulgaria<strong><br \/><\/strong><\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>","protected":false},"excerpt":{"rendered":"<p>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 &nbsp; EDITORIAL \/ \u041a\u042a\u041c \u0427\u0418\u0422\u0410\u0422\u0415\u041b\u042f &ndash; \u0441\u0442\u0440. 7 &nbsp;\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 &nbsp; EDUCATIONAL MATTERS \/ \u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e \u0410\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u0435\u043d \u0438\u043b\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u0435\u043d \u043c\u0435\u0442\u043e\u0434 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0430\u0442\u0430 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [Arithmetical or Algebraic Method in Solving Primary School Mathematical Problems] \/ \u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, \u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430, \u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430 \/ Zdravko Lalchev, Margarita Varbanova, [&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":[3290],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - 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\u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 &nbsp; EDITORIAL \/ \u041a\u042a\u041c \u0427\u0418\u0422\u0410\u0422\u0415\u041b\u042f &ndash; \u0441\u0442\u0440. 7 &nbsp;\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 &nbsp; EDUCATIONAL MATTERS \/ \u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e \u0410\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u0435\u043d \u0438\u043b\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u0435\u043d \u043c\u0435\u0442\u043e\u0434 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0430\u0442\u0430 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [Arithmetical or Algebraic Method in Solving Primary School Mathematical Problems] \/ \u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, \u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430, \u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430 \/ Zdravko Lalchev, Margarita Varbanova, [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/foreignlanguages.azbuki.bg\/matematics\/matharticles2016\/mathinfocontent012016\/\" \/>\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=\"2016-02-07T18:59:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-06-18T18:58:29+00:00\" \/>\n<meta property=\"og:image\" 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