{"id":41496,"date":"2017-02-13T10:04:08","date_gmt":"2017-02-13T07:04:08","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016-2\/1-lxx-2017\/"},"modified":"2019-06-18T21:58:28","modified_gmt":"2019-06-18T18:58:28","slug":"1-lxx-2017","status":"publish","type":"post","link":"https:\/\/bel.azbuki.bg\/en\/matematics\/matharticles2016-2\/1-lxx-2017\/","title":{"rendered":"Mathematics and Informatics, Number 1\/2017, Volume 60"},"content":{"rendered":"<p><strong><a id=\"top\"><\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><\/p>\n<p>EDITORIAL \/ \u041a\u042a\u041c \u0427\u0418\u0422\u0410\u0422\u0415\u041b\u042f \u2013 \u0441\u0442\u0440. 7<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2017\/02\/azbuki.bg_dmdocuments_Matematika_1_17_Editorial.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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/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=\"#atr01\">\u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430\u0442\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 <\/a><br \/><a href=\"#atr01\">[Development of the Didactics of Mathematics] <\/a><br \/>\/ \u041f\u0435\u0442\u044a\u0440 \u041f\u0435\u0442\u0440\u043e\u0432 \/ Petar Petrov \u2013 \u0441\u0442\u0440. 11<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2017\/02\/azbuki.bg_dmdocuments_Matematika_1_17_PetarPetrov.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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art02\">\u0417\u0430\u043d\u0438\u043c\u0430\u0442\u0435\u043b\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u041f\u043e\u0430\u0441\u043e\u043d \u0438 \u043c\u0435\u0442\u043e\u0434\u044a\u0442 \u043d\u0430 \u041f\u0435\u0440\u0435\u043b\u043c\u0430\u043d \u0437\u0430 \u0442\u044f\u0445\u043d\u043e\u0442\u043e \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u0438 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 <\/a><br \/><a href=\"#art02\">[Poisson\u2032s Amusing Problems and Perelman\u2032s Method for Their Solution and Study] <\/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, \u041c\u0438\u0440\u043e\u0441\u043b\u0430\u0432 \u0421\u0442\u043e\u0438\u043c\u0438\u0440\u043e\u0432 \/ Zdravko Lalchev, Margarita Varbanova, Miroslav Stoimirov \u2013 \u0441\u0442\u0440. 17<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2017\/02\/azbuki.bg_dmdocuments_Matematika_1_17_Lalchev_Vardanova_Stoimirov.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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art03\">\u0412\u0435\u043a\u0442\u043e\u0440\u043d\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0438 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043c\u0435\u0436\u0434\u0443 \u043b\u0438\u0446\u0430 \u043d\u0430 \u0441\u0442\u0435\u043d\u0438 \u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0432 \u043d\u044f\u043a\u043e\u0438 \u043c\u043d\u043e\u0433\u043e\u0441\u0442\u0435\u043d\u0438 <\/a><br \/><a href=\"#art03\">[Vector Product and Relations Between Side and Section Areas of Some Polyhedra] <\/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 \u2013 \u0441\u0442\u0440.\u00a050<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2017\/02\/azbuki.bg_dmdocuments_Matematika_1_17_Grozdev_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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art04\">\u041f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u0440\u0430\u043d\u0441\u0446\u0435\u043d\u0434\u0435\u043d\u0442\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f (I \u0447\u0430\u0441\u0442) <\/a><br \/><a href=\"#art04\">[Exponential and Trigonometric Functions in Transcendental Equations (Part I)] <\/a><br \/>\/ \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430 \/ Diana Stefanova \u2013 \u0441\u0442\u0440. 57<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2017\/02\/azbuki.bg_dmdocuments_Matematika_1_17_DianaStefanova.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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open 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\">\u041e\u0439\u043b\u0435\u0440\u043e\u0432\u0430 \u043f\u0440\u0430\u0432\u0430 \u0438 \u041e\u0439\u043b\u0435\u0440\u043e\u0432\u0430 \u043a\u0440\u0438\u0432\u0430 \u043d\u0430 \u0432\u043f\u0438\u0441\u0430\u043d \u043c\u043d\u043e\u0433\u043e\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u0432 \u043a\u043e\u043d\u0438\u0447\u043d\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435 <\/a><br \/><a href=\"#art05\">[An Inscribed Polygon in a Conic] <\/a><br \/>\/ \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432, \u0414\u0430\u043d\u0438\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432 \/ Veselin Nenkov, Daniel Angelov \u2013 \u0441\u0442\u0440.\u00a064<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2017\/02\/azbuki.bg_dmdocuments_Matematika_1_17_Nenkov_Angelov.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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art06\">\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u043d\u0430 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430, \u0442\u043e\u0447\u043a\u0430 \u043d\u0430 \u041c\u0438\u043a\u0435\u043b, \u0438\u043d\u0432\u0435\u0440\u0441\u043d\u0430 \u0438\u0437\u043e\u0433\u043e\u043d\u0430\u043b\u043d\u043e\u0441\u0442 <\/a><br \/><a href=\"#art06\">[Geometry of the Quadrilateral, Miquel Point, Inversion] <\/a><br \/>\/ \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432, \u0421\u0442\u0430\u043d\u0438\u0441\u043b\u0430\u0432 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432, \u0425\u0430\u0438\u043c \u0425\u0430\u0438\u043c\u043e\u0432 \/ Veselin Nenkov, Stanislav Stefanov, Haim Haimov \u2013 \u0441\u0442\u0440. 81<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2017\/02\/azbuki.bg_dmdocuments_Matematika_1_17_Nenkov_Stefanov_Haimov.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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open 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] \u2013 \u0441\u0442\u0440.\u00a094<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2017\/02\/azbuki.bg_dmdocuments_Matematika_1_17_ContestProblems.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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open 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 2, 2016 <br \/>[Solutions of the Contest Problems from Issue 2, 2016] \u2013 \u0441\u0442\u0440.\u00a096<\/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 \u2013 <\/strong>\u0441\u0442\u0440.\u00a099<\/p>\n<p>\u00a0<\/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> \u2013 \u0441\u0442\u0440.\u00a0101<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a id=\"atr01\"><\/a>\u0420\u0410\u0417\u0412\u0418\u0422\u0418\u0415 \u041d\u0410 \u041c\u0415\u0422\u041e\u0414\u0418\u041a\u0410\u0422\u0410 \u041d\u0410 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410<\/strong><\/p>\n<p>Petar Petrov<br \/>Trakia University - Stara Zagora (Bulgaria)<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d \u0435 \u0432\u044a\u0437\u0433\u043b\u0435\u0434 \u0437\u0430 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435\u0442\u043e \u043d\u0430 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430\u0442\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u041e\u0447\u0435\u0440\u0442\u0430\u043d\u0438 \u0441\u0430 \u0440\u0430\u0432\u043d\u0438\u0449\u0430 \u043d\u0430 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435, \u043e\u0441\u043d\u043e\u0432\u043d\u0438 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0438 \u0438 \u043f\u0440\u0438\u0447\u0438\u043d\u0438\u0442\u0435 \u0437\u0430 \u0442\u0440\u0443\u0434\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u0438\u043c. \u0418\u0437\u0432\u0435\u0434\u0435\u043d\u0430 \u0435 \u0438\u0434\u0435\u044f\u0442\u0430, \u0447\u0435 \u0443\u043c\u0435\u043d\u0438\u0435\u0442\u043e \u0434\u0430 \u0441\u0435 \u0440\u0435\u0448\u0430\u0432\u0430\u0442 \u0437\u0430\u0434\u0430\u0447\u0438, \u0435 \u043e\u0441\u043d\u043e\u0432\u0435\u043d \u043f\u0440\u043e\u0431\u043b\u0435\u043c \u0432 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430\u0442\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043a\u043e\u0439\u0442\u043e \u043d\u0430\u0434\u0441\u043a\u0430\u0447\u0430 \u043d\u0435\u0439\u043d\u0438\u0442\u0435 \u0433\u0440\u0430\u043d\u0438\u0446\u0438.<br \/>Keywords: skill, situation approach, heuristic activity, reflection, synergetic, skill for problem solving<\/p>\n<p><strong>DEVELOPMENT OF THE DIDACTICS OF MATHEMATICS<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>Abstract. An opinion is proposed for the development of the Didactics of Mathematics. What are described are the levels of development, main problems and the reasons for the difficulties to solve them. An idea is brought out that the skill of problem solving is a basic problem in the Didactics of Mathematics that overleaps its borders.<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Petar Petrov, DSc.<br \/>Trakia University<br \/>6000 Stara Zagora<br \/>E-mail: <a href=\"mailto:pdp@dir.bg\">pdp@dir.bg<\/a><\/p>\n<p style=\"text-align: right;\"><strong><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/strong><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong><a id=\"art02\"><\/a>\u0417\u0410\u041d\u0418\u041c\u0410\u0422\u0415\u041b\u041d\u0418\u0422\u0415 \u0417\u0410\u0414\u0410\u0427\u0418 \u041d\u0410 \u041f\u041e\u0410\u0421\u041e\u041d \u0418 \u041c\u0415\u0422\u041e\u0414\u042a\u0422 \u041d\u0410 \u041f\u0415\u0420\u0415\u041b\u041c\u0410\u041d \u0417\u0410 \u0422\u042f\u0425\u041d\u041e\u0422\u041e \u0420\u0415\u0428\u0410\u0412\u0410\u041d\u0415 \u0418 \u0418\u0417\u0421\u041b\u0415\u0414\u0412\u0410\u041d\u0415<\/strong><\/p>\n<p style=\"text-align: left;\">\u00a0<\/p>\n<p>1)\u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, 2)\u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430, 2)\u041c\u0438\u0440\u043e\u0441\u043b\u0430\u0432 \u0421\u0442\u043e\u0438\u043c\u0438\u0440\u043e\u0432<br \/>1) Sofia University<br \/>2) University of VelikoTarnovo, VelikoTarnovo, Bulgaria<\/p>\n<p>\u00a0<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u041f\u0440\u0435\u0434\u043c\u0435\u0442 \u043d\u0430 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438\u044f\u0442 \u043c\u0435\u0442\u043e\u0434 \u043d\u0430 \u041f\u0435\u0440\u0435\u043b\u043c\u0430\u043d \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u0438 \u0435\u043c\u043f\u0438\u0440\u0438\u0447\u043d\u043e \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 \u043d\u0430 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\u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438, \u0435 \u0434\u043e\u0441\u0442\u0438\u0433\u043d\u0430\u0442\u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u0430 \u0445\u0438\u043f\u043e\u0442\u0435\u0437\u0430 \u0437\u0430 \u0441\u043b\u0443\u0447\u0430\u0438 \u043d\u0430 \u043d\u0435\u0440\u0435\u0448\u0438\u043c\u043e\u0441\u0442 \u043d\u0430 \u043e\u0431\u0449\u0430\u0442\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442 \u043e\u0442 \u043d\u0435\u0439\u043d\u0438\u0442\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438. \u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u0435 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0430 \u0432\u044a\u0440\u0445\u0443 \u0435\u0434\u043d\u0430 \u043e\u0442 \u0442\u0435\u043c\u0438\u0442\u0435 \u043d\u0430 \u043a\u0443\u0440\u0441\u0430 \u043f\u043e \u0437\u0430\u043d\u0438\u043c\u0430\u0442\u0435\u043b\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043f\u0440\u0435\u0434\u043d\u0430\u0437\u043d\u0430\u0447\u0435\u043d \u0437\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438 \u2013 \u0431\u044a\u0434\u0435\u0449\u0438 \u0443\u0447\u0438\u0442\u0435\u043b\u0438. \u0422\u044f \u043c\u043e\u0436\u0435 \u0443\u0441\u043f\u0435\u0448\u043d\u043e \u0434\u0430 \u0431\u044a\u0434\u0435 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0430 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0432 \u201e\u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0438\u201c \u0443\u0441\u043b\u043e\u0432\u0438\u044f, \u0432 \u0447\u0430\u0441\u043e\u0432\u0435\u0442\u0435 \u043f\u043e \u0438\u0437\u0431\u0438\u0440\u0430\u0435\u043c\u0430 (\u0438\u043b\u0438 \u0444\u0430\u043a\u0443\u043b\u0442\u0430\u0442\u0438\u0432\u043d\u0430) \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430.<br \/>Keywords: amusing mathematics, Poisson\u2019s problems, solution, Perelman\u2019s method, empiric study, rhomboid network, overflow ray, falling and reflected ray, hypothesis<\/p>\n<p>\u00a0<\/p>\n<p><strong>POISSON\u2032S AMUSING PROBLEMS AND PERELMAN\u2032S METHOD FOR THEIR SOLUTION AND STUDY<\/strong><\/p>\n<p>Abstract. The subject of the paper is the Perelman\u2019s geometric method for solving and empiric study of a popular class of amusing problems called Poisson\u2019s problems. The main tool of investigation is a rhomboid net of a skew co-ordinate system. The problem situation is modeled geometrically and the solution of the problem is sought by the construction of \u201cPouring ray\u201d trajectory in the net. The method is described in details by simple means of analytic geometry and is presented through 8 problems for pouring. Some comments and suggestions are made in order to optimize the solutions. Empirically, it is reached a probable hypothesis on the base of the solutions of specific problems in cases of non-solvability of the general problem accounting for its parameters. The work is constructed on one of the topics of the course on Amusing Mathematics targeted on students \u2013 futur teachers. It could be applied successfully in teaching Mathematics in \u201cschool\u201d conditions during extra-curricular classes.<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Dr. Zdravko Lalchev<br \/>Faculty of Preschool and Primary Education<br \/>University of Sofia<br \/>69A, Shipchenski prohod Blvd.<br \/>1754 Sofia, Bulgaria<br \/>E-mail: <a href=\"mailto:zdravkol@abv.bg\">zdravkol@abv.bg<\/a><\/p>\n<p>Prof. Dr. Margarita Varbanova<br \/>Faculty of Mathematics and Informatics<br \/>University of Veliko Tarnovo<br \/>3A, Arh. G. Kozarev Blvd.<br \/>5000 Veliko Tarnovo, Bulgaria<br \/>E-mail: <a href=\"mailto:mvarbanova11@abv.bg\">mvarbanova11@abv.bg<\/a><\/p>\n<p>Mr. Miroslav Stoimirov, PhD student<br \/>Faculty of Mathematics and Informatics<br \/>University of Veliko Tarnovo<br \/>3A, Arh. G. Kozarev Blvd.<br \/>5000 Veliko Tarnovo, Bulgaria<br \/>E-mail: <a href=\"mailto:mstoimirov@mail.bg\">mstoimirov@mail.bg<\/a><a href=\"mailto:mstoimirov@mail.bg\"><\/a><\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a id=\"art03\"><\/a>\u0412\u0415\u041a\u0422\u041e\u0420\u041d\u041e \u041f\u0420\u041e\u0418\u0417\u0412\u0415\u0414\u0415\u041d\u0418\u0415 \u0418 \u0417\u0410\u0412\u0418\u0421\u0418\u041c\u041e\u0421\u0422\u0418 \u041c\u0415\u0416\u0414\u0423 \u041b\u0418\u0426\u0410 \u041d\u0410 \u0421\u0422\u0415\u041d\u0418 \u0418 \u0421\u0415\u0427\u0415\u041d\u0418\u042f \u0412 \u041d\u042f\u041a\u041e\u0418 \u041c\u041d\u041e\u0413\u041e\u0421\u0422\u0415\u041d\u0418<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>1) Sava Grozdev, 2) Veselin Nenkov<br \/>1)University of Finance, Business Entrepreneurship \u2013 Sofia, Bulgaria<br \/>2)\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>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0430 \u043e\u043f\u0438\u0441\u0430\u043d\u0438 \u043e\u0431\u0449\u0438 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043c\u0435\u0436\u0434\u0443 \u043b\u0438\u0446\u0430 \u043d\u0430 \u0441\u0442\u0435\u043d\u0438 \u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0432 \u043d\u044f\u043a\u043e\u0438 \u043f\u0440\u0438\u0437\u043c\u0438 \u0438 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0438. \u0420\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u0441\u0430 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438 \u0441 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435.<br \/>Keywords: vector product, pyramid, prism, parallelepiped, tetrahedron, section<\/p>\n<p>\u00a0<\/p>\n<p><strong>VECTOR PRODUCT AND RELATIONS BETWEEN SIDE AND SECTION AREAS OF SOME POLYHEDRA<\/strong><\/p>\n<p>Abstract. The paper describes general relations between areas of sides and sections in some prisms and pyramids. The results are obtained by the use of vector product.<\/p>\n<p>Prof. Sava Grozdev, DSc.<br \/>University of Finance, Business and Entrepreneurship<br \/>1, Gusla Str.<br \/>1618 Sofia, Bulgaria<br \/>E-mail: <a href=\"mailto:sava.grozdev@gmail.com\">sava.grozdev@gmail.com<\/a><\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof. <br \/>Technical College, Lovech<br \/>31, Sajko Saev Str.<br \/>5500 Lovech, Bulgaria<br \/>E-mail: <a href=\"mailto:vnenkov@mail.bg\">vnenkov@mail.bg<\/a><a href=\"mailto:vnenkov@mail.bg\"><\/a><\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a id=\"art04\"><\/a>\u041f\u041e\u041a\u0410\u0417\u0410\u0422\u0415\u041b\u041d\u0418 \u0418 \u0422\u0420\u0418\u0413\u041e\u041d\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0418 \u0424\u0423\u041d\u041a\u0426\u0418\u0418 \u0412 \u0422\u0420\u0410\u041d\u0421\u0426\u0415\u041d\u0414\u0415\u041d\u0422\u041d\u0418 \u0423\u0420\u0410\u0412\u041d\u0415\u041d\u0418\u042f (I \u0427\u0410\u0421\u0422)<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>Diana Stefanova<\/p>\n<p>\u00a0<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0442 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u043e\u0442 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0438\u0442\u043e \u0443\u0447\u0430\u0441\u0442\u0432\u0430\u0442 \u0432 \u0442\u0440\u0430\u043d\u0441\u0446\u0435\u043d\u0434\u0435\u043d\u0442\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0420\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u0441\u0435 \u043f\u043e\u0434\u0445\u043e\u0434\u0438 \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u0438\u043c.<br \/>Keywords: transcendental equation, exponential equation, trigonometric <br \/>equation, problem solving<\/p>\n<p><strong>EXPONENTIAL AND TRIGONOMETRIC FUNCTIONS\u00a0IN TRANSCENDENTAL EQUATIONS (PART I)<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>Abstract. The paper proposes combinations of exponential and trigonometric functions, which are included in transcendental equations. Approaches for their solutions are considered.<\/p>\n<p>Dr. Diana Stefanova<br \/>Teacher in Mathematics<br \/>Asenovgrad<br \/>E-mail: <a href=\"mailto:dianastefan@abv.bg\">dianastefan@abv.bg<\/a><a href=\"mailto:dianastefan@abv.bg\"><\/a><\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a id=\"art05\"><\/a>\u041e\u0419\u041b\u0415\u0420\u041e\u0412\u0410 \u041f\u0420\u0410\u0412\u0410 \u0418 \u041e\u0419\u041b\u0415\u0420\u041e\u0412\u0410 \u041a\u0420\u0418\u0412\u0410 \u041d\u0410 \u0412\u041f\u0418\u0421\u0410\u041d \u041c\u041d\u041e\u0413\u041e\u042a\u0413\u042a\u041b\u041d\u0418\u041a \u0412 \u041a\u041e\u041d\u0418\u0427\u041d\u041e \u0421\u0415\u0427\u0415\u041d\u0418\u0415<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432, \u0414\u0430\u043d\u0438\u0435\u043b \u0410\u043d\u0433\u0435\u043b\u043e\u0432<br \/>\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>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u043f\u0440\u043e\u0441\u043b\u0435\u0434\u044f\u0432\u0430 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u043e\u0442\u043e \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 \u0438\u0434\u0435\u044f\u0442\u0430 \u0437\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u043d\u0435 \u043d\u0430 \u043f\u043e\u043d\u044f\u0442\u0438\u044f\u0442\u0430 \u041e\u0439\u043b\u0435\u0440\u043e\u0432\u0430 \u043f\u0440\u0430\u0432\u0430 \u0438 \u041e\u0439\u043b\u0435\u0440\u043e\u0432\u0430 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 \u043d\u0430 \u0432\u043f\u0438\u0441\u0430\u043d \u0432 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 \u043c\u043d\u043e\u0433\u043e\u044a\u0433\u044a\u043b\u043d\u0438\u043a, \u043a\u043e\u044f\u0442\u043e \u043f\u043e \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d \u043d\u0430\u0447\u0438\u043d \u0432\u043e\u0434\u0438 \u0434\u043e \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u044f \u043d\u0430 \u041e\u0439\u043b\u0435\u0440\u043e\u0432\u0430 \u043f\u0440\u0430\u0432\u0430 \u0438 \u041e\u0439\u043b\u0435\u0440\u043e\u0432\u0430 \u043a\u0440\u0438\u0432\u0430 \u0437\u0430 \u0432\u043f\u0438\u0441\u0430\u043d \u0432 \u043a\u043e\u043d\u0438\u0447\u043d\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435 \u043c\u043d\u043e\u0433\u043e\u044a\u0433\u044a\u043b\u043d\u0438\u043a. \u0418\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0438\u044f\u0442\u0430 \u043d\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438\u0442\u0435 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438 \u0441\u0430 \u043f\u043e\u0434\u043f\u043e\u043c\u043e\u0433\u043d\u0430\u0442\u0438 \u0441 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438\u044f \u043f\u0440\u043e\u0434\u0443\u043a\u0442 THE GEOMETER\u2019S SKETCHPAD (GSP).<br \/>Keywords: conic, center of gravity, orthocenter, polygon, Euler line, Euler curve, GSP<\/p>\n<p><strong>EULER LINE AND EULER CURVE OF AN INSCRIBED POLYGON IN A CONIC<\/strong><\/p>\n<p>Abstract. The paper follows the successive development of the idea to define the notions of Euler line and Euler curve of an inscribed polygon in a circle, which leads in a natural way to the construction of Euler line and Euler curve of an inscribed polygon in a conic. Various configurations are examined by the help of the computer program \u201cTHE GEOMETER\u2019S SKETCHPAD\u201d (GSP).<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof. <br \/>Technical College, Lovech<\/p>\n<p>31, Sajko Saev Str.<br \/>5500 Lovech, Bulgaria<br \/>E-mail: <a href=\"mailto:vnenkov@mail.bg\">vnenkov@mail.bg<\/a><\/p>\n<p>Mr. Daniel Angelov, Assist. Prof.<br \/>Technical College, Lovech<br \/>31, Sajko Saev St.<br \/>5500 Lovech, Bulgaria <br \/>E-mail: <a href=\"mailto:dangelovbg@mail.bg\">dangelovbg@mail.bg<\/a><a href=\"mailto:dangelovbg@mail.bg\"><\/a><\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p><strong><a id=\"art06\"><\/a>\u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u042f \u041d\u0410 \u0427\u0415\u0422\u0418\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u041a\u0410,\u00a0\u0422\u041e\u0427\u041a\u0410 \u041d\u0410 \u041c\u0418\u041a\u0415\u041b, \u0418\u041d\u0412\u0415\u0420\u0421\u041d\u0410 \u0418\u0417\u041e\u0413\u041e\u041d\u0410\u041b\u041d\u041e\u0421\u0422<\/strong><\/p>\n<p>1)\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432, 2)\u0421\u0442\u0430\u043d\u0438\u0441\u043b\u0430\u0432 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432, \u0425\u0430\u0438\u043c \u0425\u0430\u0438\u043c\u043e\u0432<br \/>1)\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u041b\u043e\u0432\u0435\u0447<br \/>2) Technical University \u2013 Sofia<\/p>\n<p>\u00a0<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0430 \u043e\u043f\u0438\u0441\u0430\u043d\u0438 \u043d\u044f\u043a\u043e\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043d\u0430 \u0442\u043e\u0447\u043a\u0430\u0442\u0430 \u043d\u0430 \u041c\u0438\u043a\u0435\u043b \u0437\u0430 \u043f\u044a\u043b\u043d\u0438\u044f \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u0438 \u0432\u0440\u044a\u0437\u043a\u0438\u0442\u0435 \u045d \u0441 \u0434\u0440\u0443\u0433\u0438 \u0437\u0430\u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0435\u043b\u043d\u0438 \u0442\u043e\u0447\u043a\u0438 \u043d\u0430 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430.<br \/>Keywords: quadrilateral, circumcircle, Miquel point, inversion, isogonality<\/p>\n<p>\u00a0<\/p>\n<p><strong>GEOMETRY OF THE QUADRILATERAL,\u00a0MIQUEL POINT, INVERSION ISOGONALITY<\/strong><\/p>\n<p>Abstract. The paper describes some properties of Miquel point for the complete quadrilateral and relations with other notable points of the quadrilateral.<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof. <br \/>Technical College Lovech<br \/>31, Sajko Saev Str.<br \/>5500 Lovech, Bulgaria<br \/>E-mail: <a href=\"mailto:vnenkov@mail.bg\">vnenkov@mail.bg<\/a><\/p>\n<p>Mr. Stanislav Stefanov, PhD student<br \/>Technical University Sofia<br \/>E-mail: <a href=\"mailto:stanislav.toshkov@abv.bg\">stanislav.toshkov@abv.bg<\/a><\/p>\n<p>Mr. Haim Haimov, Researcher<br \/>16, Bratya Shkorpil Str.<br \/>9000 Varna<\/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 EDITORIAL \/ \u041a\u042a\u041c \u0427\u0418\u0422\u0410\u0422\u0415\u041b\u042f \u2013 \u0441\u0442\u0440. 7\u00a0\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \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\u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 \u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430\u0442\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [Development of the Didactics of Mathematics] \/ \u041f\u0435\u0442\u044a\u0440 \u041f\u0435\u0442\u0440\u043e\u0432 \/ Petar Petrov \u2013 \u0441\u0442\u0440. 11\u00a0\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \u00a0 \u0417\u0430\u043d\u0438\u043c\u0430\u0442\u0435\u043b\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u041f\u043e\u0430\u0441\u043e\u043d \u0438 \u043c\u0435\u0442\u043e\u0434\u044a\u0442 \u043d\u0430 \u041f\u0435\u0440\u0435\u043b\u043c\u0430\u043d \u0437\u0430 \u0442\u044f\u0445\u043d\u043e\u0442\u043e \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u0438 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 [&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 optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>&quot;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&quot;, \u043a\u043d\u0438\u0436\u043a\u0430 1, \u0433\u043e\u0434\u0438\u043d\u0430 LX, 2017 - \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:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles2016-2\/1-lxx-2017\/\" 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\u043c\u0435\u0442\u043e\u0434\u0438\u043a\u0430\u0442\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [Development of the Didactics of Mathematics] \/ \u041f\u0435\u0442\u044a\u0440 \u041f\u0435\u0442\u0440\u043e\u0432 \/ Petar Petrov \u2013 \u0441\u0442\u0440. 11\u00a0\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \u00a0 \u0417\u0430\u043d\u0438\u043c\u0430\u0442\u0435\u043b\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u041f\u043e\u0430\u0441\u043e\u043d \u0438 \u043c\u0435\u0442\u043e\u0434\u044a\u0442 \u043d\u0430 \u041f\u0435\u0440\u0435\u043b\u043c\u0430\u043d \u0437\u0430 \u0442\u044f\u0445\u043d\u043e\u0442\u043e \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u0438 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 [&hellip;]\" \/>\n<meta property=\"og:url\" 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