{"id":38176,"date":"2013-02-27T21:59:29","date_gmt":"2013-02-27T18:59:29","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2013\/"},"modified":"2019-06-18T21:59:01","modified_gmt":"2019-06-18T18:59:01","slug":"matematika-i-informatika-knizhka-1-godina-lvi-2013-2","status":"publish","type":"post","link":"https:\/\/science.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2013-2\/","title":{"rendered":"Mathematics and Informatics, Number 1\/2013, Volume 56"},"content":{"rendered":"<p><strong>\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS<\/strong><\/p>\n<p><strong><br \/>70th anniversary - Prof. Gencho Skordev<\/strong> &#8211; \u0441\u0442\u0440. 9<\/p>\n<p style=\"text-align: center;\"><a href=\"\/en\/index.php\/?option=com_docman&amp;task=doc_download&amp;gid=839&amp;Itemid=365\"><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><a href=\"#art01\">\u0427\u0442\u043e \u0411\u043e\u043b\u044c\u0448\u043e\u0435: \u03c0% \u043e\u0442 e \u0438\u043b\u0438 e% \u043e\u0442 \u03c0?<\/a><br \/><a href=\"#art01\"> [What is Greater: \u03c0% of e or e% of \u03c0?] \/ <\/a><br \/><em>\u041d. \u0420\u043e\u0437\u043e\u0432 \/ N. Rozov<\/em> &#8211; \u0441\u0442\u0440. 17<\/p>\n<p style=\"text-align: center;\"><a href=\"\/en\/index.php\/?option=com_docman&amp;task=doc_download&amp;gid=864&amp;Itemid=365\"><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><a href=\"#art02\">\u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432\u044a\u0440\u0445\u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0440\u0435\u0431\u0443\u0441\u0438 \u0438\u043b\u0438\u2026\u0415\u043c\u043f\u0438\u0440\u0438\u0447\u0435\u043d \u043f\u043e\u0434\u0445\u043e\u0434<\/a><br \/><a href=\"#art02\">\u0437\u0430 \u043e\u0446\u0435\u043d\u043a\u0430 \u043d\u0430 \u0432\u0440\u0435\u043c\u0435\u0442\u043e \u0437\u0430 \u0438\u0437\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438 <\/a><br \/><a href=\"#art02\">[Computing Problems on&nbsp;Mathematical Puzzles or&#8230; An Empirical Approach <\/a><br \/><a href=\"#art02\">for Evaluating the Program&nbsp;Execution Time] \/ <\/a><br \/><em>\u041f. \u0410\u0437\u044a\u043b\u043e\u0432 \/ P. Azalov<\/em> &#8211; \u0441\u0442\u0440. 33<\/p>\n<p style=\"text-align: center;\"><a href=\"\/en\/index.php\/?option=com_docman&amp;task=doc_download&amp;gid=830&amp;Itemid=365\"><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><a href=\"#art03\">\u041f\u043e \u043f\u044a\u0442\u044f \u043a\u044a\u043c \u043f\u044a\u0440\u0432\u0430\u0442\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u043e-\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0430 \u0435\u043d\u0446\u0438\u043a\u043b\u043e\u043f\u0435\u0434\u0438\u044f <\/a><br \/><a href=\"#art03\">[Towards the&nbsp;First Computer-Generated Encyclopedia] \/ <\/a><br \/><em>\u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev, \u0414. \u0414\u0435\u043a\u043e\u0432 \/ D. Dekov<\/em> &#8211; \u0441\u0442\u0440. 49<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"\/en\/index.php\/?option=com_docman&amp;task=doc_download&amp;gid=860&amp;Itemid=365\"><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><a href=\"#art04\">Several Proofs of an Algebraic Inequality <\/a><br \/><a href=\"#art04\">[\u041d\u044f\u043a\u043e\u043b\u043a\u043e \u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430 \u043d\u0430 \u0415\u0434\u043d\u043e&nbsp;\u0410\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u043d\u043e \u041d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e] \/<\/a> <br \/><em>\u0160. Arslanagi\u0107 \/ \u0428. \u0410\u0440\u0441\u043b\u0430\u043d\u0430\u0433\u0438\u0447<\/em> &#8211; \u0441\u0442\u0440. 60<\/p>\n<p style=\"text-align: center;\"><a href=\"\/en\/index.php\/?option=com_docman&amp;task=doc_download&amp;gid=856&amp;Itemid=365\"><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\" \/>Open the full text<\/a><\/p>\n<p><a href=\"#art05\">\u0412\u0438\u0440\u0442\u0443\u0430\u043b\u043d\u0430 \u0440\u0435\u0430\u043b\u043d\u043e\u0441\u0442 \u2013 \u0435\u0434\u0438\u043d \u043d\u043e\u0432 \u043f\u043e\u0433\u043b\u0435\u0434 \u043a\u044a\u043c \u0441\u044a\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0442\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 <\/a><br \/><a href=\"#art05\">[Virtual&nbsp;Reality \u2013 A New Vision On The Contemporary Education] \/ <\/a><br \/><em>\u0414. \u041c\u0438\u043d\u043a\u043e\u0432\u0441\u043a\u0430 \/ D. Minkovska<\/em> &#8211; \u0441\u0442\u0440. 64<\/p>\n<p style=\"text-align: center;\"><a href=\"\/en\/index.php\/?option=com_docman&amp;task=doc_download&amp;gid=862&amp;Itemid=365\"><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><a href=\"#art06\">\u0418\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u043d\u0438 \u0438 \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u0438 \u043c\u043e\u0434\u0435\u043b\u0438 \u0437\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435 <\/a><br \/><a href=\"#art06\">\u043d\u0430 \u0443\u0447\u0435\u0431\u043d\u043e \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u043f\u043e \u0434\u0438\u0441\u0446\u0438\u043f\u043b\u0438\u043d\u0430\u0442\u0430 \u201e\u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438\u043c\u0440\u0435\u0436\u0438 \u0438 \u043a\u043e\u043c\u0443\u043d\u0438\u043a\u0430\u0446\u0438\u0438\u201c<\/a><br \/><a href=\"#art06\"> [UsingDynamic&nbsp;And Interactive Models For Curriculum Presentation <\/a><br \/><a href=\"#art06\">Of A \u201eComputer Networks And&nbsp;Communications\u201c Course] \/<\/a> <br \/><em>\u0413. \u0421\u0442\u043e\u0438\u0446\u043e\u0432 \/ G. Stoitsov, \u041a. \u0413\u044a\u0440\u043e\u0432 \/ K. Garov<\/em> &#8211; \u0441\u0442\u0440. 73<\/p>\n<p style=\"text-align: center;\"><a href=\"\/en\/index.php\/?option=com_docman&amp;task=doc_download&amp;gid=865&amp;Itemid=365\"><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><strong> \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418 \/ CONTEST PROBLEMS<\/strong><br \/><strong>\u0420\u0443\u0431\u0440\u0438\u043a\u0430\u0442\u0430 \u0441\u0435 \u0432\u043e\u0434\u0438 \u043e\u0442 \u0434-\u0440 \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \u0438 \u0434-\u0440 \u0416\u0438\u0432\u043a\u043e \u0416\u0435\u043b\u0435\u0432<\/strong><\/p>\n<p>\u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f &#8211; \u0441\u0442\u0440. 84<br \/>\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 2, 2012 &#8211; \u0441\u0442\u0440. 85<\/p>\n<p style=\"text-align: center;\"><a style=\"text-align: center;\" href=\"\/en\/index.php\/?option=com_docman&amp;task=doc_download&amp;gid=831&amp;Itemid=365\"><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>\u0412 \u043d\u043e\u0432\u0438\u0442\u0435 \u0431\u0440\u043e\u0435\u0432\u0435 \u043d\u0430 \u0441\u043f\u0438\u0441\u0430\u043d\u0438\u044f\u0442\u0430 \u043d\u0430 \u0438\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e \u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c \u0447\u0435\u0442\u0435\u0442\u0435 \/ <\/strong><br \/><strong>Read in&nbsp;the latest issues of the \u201eAz Buki\u201c magazines<\/strong> &#8211; \u0441\u0442\u0440. 88<\/p>\n<p style=\"text-align: center;\"><a href=\"\/en\/index.php\/?option=com_docman&amp;task=doc_download&amp;gid=863&amp;Itemid=365\"><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><strong>\u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415 \/ GUIDE FOR AUTHORS<\/strong> &#8211; \u0441\u0442\u0440. 90<\/p>\n<p style=\"text-align: center;\"><a href=\"\/en\/index.php\/?option=com_docman&amp;task=doc_download&amp;gid=861&amp;Itemid=365\"><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<hr \/>\n<p><strong><a name=\"art01\">&nbsp;<\/a>\u0427\u0422\u041e \u0411\u041e\u041b\u042c\u0428\u0415: \u03c0% \u043e\u0442 e \u0438\u043b\u0438 e% \u043e\u0442 \u03c0?<\/strong><\/p>\n<p><strong><br \/>\u041d\u0438\u043a\u043e\u043b\u0430\u0439 \u0420\u043e\u0437\u043e\u0432<\/strong><\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u043e\u043f\u044b\u0442 \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u043e\u0432 \u0432 \u0448\u043a\u043e\u043b\u0435. \u041e\u0431\u043e\u0441\u043d\u043e\u0432\u044b\u0432\u0430\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u0433\u043b\u0430\u0432\u043d\u0430\u044f \u0442\u0440\u0443\u0434\u043d\u043e\u0441\u0442\u044c \u0437\u0430\u0434\u0430\u0447 \u043d\u0430 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u044b \u0432\u043e\u0432\u0441\u0435 \u043d\u0435 \u0432 \u0441\u0430\u043c\u0438\u0445 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0430\u0445, \u0430&nbsp;\u0432 \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0442\u043e\u0447\u043d\u043e\u0433\u043e \u0438 \u0447\u0451\u0442\u043a\u043e\u0433\u043e \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0438, \u043e \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0438\u0434\u0451\u0442&nbsp;\u0440\u0435\u0447\u044c \u0432 \u0437\u0430\u0434\u0430\u0447\u0435. \u0418\u043c\u0435\u043d\u043d\u043e \u0440\u0430\u0437\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u044e \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u044f \u0437\u0430\u0434\u0430\u0447\u0438 \u0438 \u043d\u0430\u0434\u043e \u0443\u0434\u0435\u043b\u044f\u0442\u044c \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435. \u0414\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u0442\u043e\u043b\u044c\u043a\u043e \u0432 \u043a\u0443\u0440\u0441\u0435 \u044d\u043a\u043e\u043d\u043e\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0437\u043d\u0430\u043d\u0438\u0439 \u0435\u0441\u0442\u044c \u0440\u0435\u0430\u043b\u044c\u043d\u0430\u044f \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0441\u0432\u044f\u0437\u0430\u0442\u044c \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u044b \u0441 \u0430\u043a\u0442\u0443\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0434\u043b\u044f \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438 \u043d\u043e\u0432\u044b\u043c\u0438 \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u043e\u043d\u044f\u0442\u0438\u044f\u043c\u0438.<\/p>\n<p><em>Keywords:<\/em> education, percentage, practical problems<\/p>\n<p><strong>WHAT IS GREATER: \u03c0% from e or e% from \u03c0?<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The paper considers the experience in the perception of percentages by students. It is grounded that the main difficulty in solving problems with percentages is not at all in the percentages themselves but in the complexity of a clear and exact understanding of the practical situation that is modelled by a respective problem. Thus, special attention should be paid to the clarification of the problem content. It is proved that a real possibility to connect percentages with actual fundamental notions of the contemporary reality could be found in Economics course knowledge.<\/p>\n<p><strong>Nickolay Rozov,Professor, DSc in Mathematics<\/strong><br \/><em>Corresponding Member of the Russian Academy of Education<\/em><br \/><em>Dean of the Pedagogical Faculty<\/em><br \/><em>Moscow State University \u201eV. Lomonosov\u201c<\/em><\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<p style=\"text-align: right;\">&nbsp;<\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p><strong><a name=\"art02\">&nbsp;<\/a>\u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0422\u0418\u0427\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418 \u0412\u042a\u0420\u0425\u0423 <\/strong><strong>\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u0418 \u0420\u0415\u0411\u0423\u0421\u0418&#8230; \u0418\u041b\u0418 \u0415\u041c\u041f\u0418\u0420\u0418\u0427\u0415\u041d <\/strong><br \/><strong>\u041f\u041e\u0414\u0425\u041e\u0414 \u0417\u0410 \u041e\u0426\u0415\u041d\u041a\u0410 \u041d\u0410 \u0412\u0420\u0415\u041c\u0415\u0422\u041e <\/strong><strong>\u0417\u0410 \u0418\u0417\u041f\u042a\u041b\u041d\u0415\u041d\u0418\u0415 \u041d\u0410 \u041f\u0420\u041e\u0413\u0420\u0410\u041c\u0418 <\/strong><\/p>\n<p><strong><br \/>Pavel Azalov<\/strong><\/p>\n<p><strong><br \/>Abstract.<\/strong> \u041e\u0441\u043d\u043e\u0432\u0435\u043d \u0430\u043a\u0446\u0435\u043d\u0442 \u0432 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u0440\u0435\u0441\u043c\u044f\u0442\u0430\u043d\u0435 \u043d\u0430 \u0432\u0440\u0435\u043c\u0435\u0442\u043e \u0437\u0430 \u0438\u0437\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438. \u0421 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u043e\u0442 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0440\u0435\u0431\u0443\u0441\u0438 \u0441\u0435 \u0438\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0430 \u043a\u0430\u043a \u0432\u0440\u0435\u043c\u0435\u0442\u043e \u0437\u0430 \u0438\u0437\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \u0435\u0434\u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u0437\u0430\u0432\u0438\u0441\u0438 \u043d\u0430\u0439-\u0432\u0435\u0447\u0435 \u043e\u0442 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0438\u044f \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u044a\u043c. \u041e\u043f\u0438\u0441\u0430\u043d\u0438 \u0441\u0430 \u0442\u0440\u0438 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u044a\u043c\u0430, \u043a\u043e\u0438\u0442\u043e \u0440\u0435\u0448\u0430\u0432\u0430\u0442 \u0435\u0434\u0438\u043d \u0438 \u0441\u044a\u0449 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0440\u0435\u0431\u0443\u0441. \u041f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u0438 \u0441\u0430 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u043e\u0442 \u043f\u0440\u0435\u0441\u043c\u0435\u0442\u043d\u0430\u0442\u0438\u0442\u0435 \u0432\u0440\u0435\u043c\u0435\u043d\u0430 \u0437\u0430 \u0438\u0437\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0442\u0435, \u043d\u0430\u043f\u0438\u0441\u0430\u043d\u0438 \u043f\u043e \u0442\u0435\u0437\u0438 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438 \u0432 \u0442\u0430\u0431\u043b\u0438\u0447\u0435\u043d \u0438 \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u043d \u0444\u043e\u0440\u043c\u0430\u0442. \u0412 \u043a\u0440\u0430\u044f \u043d\u0430 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0438 \u043d\u044f\u043a\u043e\u043b\u043a\u043e \u0438\u0434\u0435\u0438 \u0437\u0430 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u044f \u043f\u0440\u043e\u0435\u043a\u0442.<\/p>\n<p><em>Keywords:<\/em> program execution time, solving math puzzles, emperical approach<\/p>\n<p><strong>COMPUTING PROBLEMS ON MATHEMATICAL PUZZLES OR\u2026&nbsp;<\/strong><strong>AN EMPIRICAL APPROACH FOR EVALUATING&nbsp;<br \/><\/strong><strong>THE PROGRAM EXECUTION TIME<\/strong><\/p>\n<p><strong><br \/>Abstract.<\/strong> The main focus of this paper is the calculation of the program execution time. By using math puzzles as examples, it is shown how the program execution time depends primarily on the algorithm. We present three algorithms for solving the same math puzzle. For the programs using these algorithms, the execution time is displayed in both tabular and graphical format. A set of open questions and problems is included in the last section.<\/p>\n<p><strong>Pavel Azalov<\/strong><br \/><em>Associate Prof. of Computer Science, Ph.D.<\/em><br \/><em>Pennsylvania State University, USA<\/em><\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<hr \/>\n<p><strong><a name=\"art03\">&nbsp;<\/a>\u041f\u041e \u041f\u042a\u0422\u042f \u041a\u042a\u041c \u041f\u042a\u0420\u0412\u0410\u0422\u0410 <\/strong><strong>\u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420\u041d\u041e-\u0413\u0415\u041d\u0415\u0420\u0418\u0420\u0410\u041d\u0410 \u0415\u041d\u0426\u0418\u041a\u041b\u041e\u041f\u0415\u0414\u0418\u042f<\/strong><\/p>\n<p><strong><br \/>Sava Grozdev<br \/>\u0414\u0435\u043a\u043e \u0414\u0435\u043a\u043e\u0432<\/strong><\/p>\n<p><strong><br \/>Abstract.<\/strong> \u0410\u0432\u0442\u043e\u0440\u0438\u0442\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u0442 \u0441\u044a\u0437\u0434\u0430\u0434\u0435\u043d\u0430\u0442\u0430 \u043e\u0442 \u0442\u044f\u0445 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u201e\u041e\u0442\u043a\u0440\u0438\u0432\u0430\u0442\u0435\u043b\u201c, \u043f\u0440\u0435\u0434\u043d\u0430\u0437\u043d\u0430\u0447\u0435\u043d\u0430 \u0434\u0430 \u043e\u0442\u043a\u0440\u0438\u0432\u0430 \u043d\u043e\u0432\u0438 \u0442\u0435\u043e\u0440\u0435\u043c\u0438 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0442\u0430 \u043d\u0430 \u0415\u0432\u043a\u043b\u0438\u0434\u043e\u0432\u0430\u0442\u0430 &nbsp;\u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f. \u041f\u0440\u043e\u0433\u0440\u0430\u043c\u0430\u0442\u0430 \u043c\u043e\u0436\u0435 \u0434\u0430 \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 \u0438 \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u0435, \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e, \u0438\u0437\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0438 \u0435\u043a\u0441\u0442\u0440\u0435\u043c\u0430\u043b\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438. \u0422\u044f \u0435 &nbsp;\u043f\u043e\u0434\u0445\u043e\u0434\u044f\u0449\u0430 \u0437\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0441 \u043f\u043e\u0432\u0438\u0448\u0435\u043d \u0438\u043d\u0442\u0435\u0440\u0435\u0441 \u043a\u044a\u043c \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0442\u0430, \u0437\u0430 \u043a\u0440\u044a\u0436\u043e\u0447\u043d\u0430 \u0440\u0430\u0431\u043e\u0442\u0430, \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430 \u0437\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0438, \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430 \u043d\u0430 \u0441\u0442\u0430\u0442\u0438\u0438 \u0437\u0430 \u0443\u0447\u0430\u0441\u0442\u0438\u0435 \u0432 \u0443\u0447\u0435\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u044a\u0441\u0442\u0435\u0437\u0430\u043d\u0438\u044f \u0438 \u0434\u0440\u0443\u0433\u0438. \u0412 \u0442\u0430\u0437\u0438 \u0441\u0442\u0430\u0442\u0438\u044f \u043a\u0430\u0442\u043e \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430 \u0444\u0440\u0430\u0433\u043c\u0435\u043d\u0442 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0430\u0442\u0430 \u0437\u0430 \u043f\u043e\u0441\u0442\u0440\u043e\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u043d\u0430 \u041c\u0430\u043b\u0444\u0430\u0442\u0438 \u0438 \u0441\u0435 \u0434\u0430\u0432\u0430 \u043d\u043e\u0432 \u043f\u043e\u0434\u0445\u043e\u0434 \u043a\u044a\u043c \u0442\u0430\u0437\u0438 \u0437\u0430\u0434\u0430\u0447\u0430. \u041e\u0442\u0431\u0435\u043b\u044f\u0437\u0432\u0430 \u0441\u0435, \u0447\u0435 \u0432\u044a\u0432\u0435\u0436\u0434\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u201e\u041e\u0442\u043a\u0440\u0438\u0432\u0430\u0442\u0435\u043b\u201c \u0437\u0430 \u043f\u044a\u0440\u0432\u0438 \u043f\u044a\u0442 \u0434\u0430\u0432\u0430 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442 \u0437\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438\u0447\u0435\u043d \u043f\u043e\u0434\u0445\u043e\u0434 \u043a\u044a\u043c \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u0435 \u0441 \u043b\u0438\u043d\u0438\u0439\u043a\u0430 \u0438 \u043f\u0435\u0440\u0433\u0435\u043b \u0432 \u0415\u0432\u043a\u043b\u0438\u0434\u043e\u0432\u0430\u0442\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f.<\/p>\n<p><em>Keywords:<\/em> computer-generated mathematics, euclidean geometry, Malfatti construction problem, mathematical olympiad<\/p>\n<p><strong>TOWARDS THE FIRST&nbsp;<\/strong><strong>COMPUTER-GENERATED ENCYCLOPEDIA<\/strong><\/p>\n<p><strong><br \/>Abstract.<\/strong> The authors present their computer program \u201eDiscoverer\u201c, intended to discover new theorems in the field of Euclidean geometry. Also, the program could be used in construction problems, to find proofs of theorems, to solve computational problems and extremal problems. It is suitable for high school students with special interest to Mathematics, for circle activities and preparation for participation in Mathematical Olympiads, for preparation of scientific papers for student competitions and others. A possible application of the computer program is considered in the present paper concerning a fragment of the problem for Malfatti circle constructions, thus proposing a new approach. It is stated that the introduction of \u201eDiscoverer\u201c gives for the first time a possibility for an algorithmic approach to ruler-compass construction problems in Euclidean geometry.<\/p>\n<p><strong>Sava Grozdev<\/strong><br \/><em>Professor, Doctor in Mathematics, DSc in Pedagogy<\/em><br \/><em>Institute of Mathematics and Informatics \u2013 BAS<\/em><br \/><em>Sofia, Bulgaria<\/em><\/p>\n<p><strong>Deko Dekov<\/strong><br \/><em>Associated Professor, PhD in Mathematics<\/em><br \/><em>Stara Zagora<\/em><\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<hr \/>\n<p><strong><a name=\"art04\">&nbsp;<\/a>SEVERAL PROOFS OF <\/strong><strong>AN ALGEBRAIC INEQUALITY<\/strong><\/p>\n<p><strong><br \/>\u0160efket Arslanagi\u0107<\/strong><\/p>\n<p><strong><br \/>Abstract<\/strong>. A recently published algebraic inequality is discussed and three new proofs of it are proposed. The paper is of methodological character.<\/p>\n<p><em>Keywords:<\/em> inequality, problem solving, proof.<\/p>\n<p><strong>\u041d\u042f\u041a\u041e\u041b\u041a\u041e \u0414\u041e\u041a\u0410\u0417\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u0410&nbsp;<\/strong><strong>\u041d\u0410 \u0415\u0414\u041d\u041e \u0410\u041b\u0413\u0415\u0411\u0420\u0418\u0427\u041d\u041e \u041d\u0415\u0420\u0410\u0412\u0415\u041d\u0421\u0422\u0412\u041e<\/strong><\/p>\n<p><strong><br \/>\u0428\u0435\u0444\u043a\u0435\u0442 \u0410\u0440\u0441\u043b\u0430\u043d\u0430\u0433\u0438\u0447<\/strong><\/p>\n<p><strong><br \/>Abstract.<\/strong> \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u043e \u0435 \u0435\u0434\u043d\u043e \u043d\u0430\u0441\u043a\u043e\u0440\u043e \u043f\u0443\u0431\u043b\u0438\u043a\u0443\u0432\u0430\u043d\u043e \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u043d\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0442\u0432\u043e \u0438 \u0441\u0430 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438 \u0442\u0440\u0438 \u043d\u0435\u0433\u043e\u0432\u0438 \u043d\u043e\u0432\u0438 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430. \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u0441 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440.<\/p>\n<p><strong>\u0160efket Arslanagi\u0107<\/strong><br \/><em>Professor, Doctor in Mathematics<\/em><br \/><em>Faculty of Mathematics and Natural Sciences<\/em><br \/><em>University of Sarajevo<\/em><br \/><em>Sarajevo, Bosnia and Herzegovina<\/em><\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<hr \/>\n<p><strong><a name=\"art05\">&nbsp;<\/a>\u0412\u0418\u0420\u0422\u0423\u0410\u041b\u041d\u0410\u0422\u0410 \u0420\u0415\u0410\u041b\u041d\u041e\u0421\u0422 \u2013 \u0415\u0414\u0418\u041d \u041d\u041e\u0412 \u041f\u041e\u0413\u041b\u0415\u0414 <\/strong><strong>\u041a\u042a\u041c \u0421\u042a\u0412\u0420\u0415\u041c\u0415\u041d\u041d\u041e\u0422\u041e \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415<\/strong><\/p>\n<p><strong><br \/>\u0414\u0430\u043d\u0438\u0435\u043b\u0430 \u041c\u0438\u043d\u043a\u043e\u0432\u0441\u043a\u0430<\/strong><\/p>\n<p><strong><br \/>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0442\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f, \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u0438 \u0438 \u043f\u0440\u0438\u043d\u0446\u0438\u043f\u0438 \u043d\u0430 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u044f\u0442\u0430 \u0432\u0438\u0440\u0442\u0443\u0430\u043b\u043d\u0430 \u0440\u0435\u0430\u043b\u043d\u043e\u0441\u0442. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0441\u0430 \u043d\u044f\u043a\u043e\u0438 \u043e\u0442 \u0441\u0440\u0435\u0434\u0438\u0442\u0435 \u0437\u0430 \u0432\u0438\u0440\u0442\u0443\u0430\u043b\u043d\u0430 \u0440\u0435\u0430\u043b\u043d\u043e\u0441\u0442 \u0438 \u0442\u044f\u0445\u043d\u043e\u0442\u043e \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435. \u041e\u043f\u0438\u0441\u0430\u043d\u0438 \u0441\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0442\u0435 \u043f\u0440\u0438\u043d\u0446\u0438\u043f\u0438 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u0432\u0438\u0440\u0442\u0443\u0430\u043b\u043d\u0430\u0442\u0430 \u0440\u0435\u0430\u043b\u043d\u043e\u0441\u0442 \u043e\u0442 \u0433\u043b\u0435\u0434\u043d\u0430 \u0442\u043e\u0447\u043a\u0430 \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u0442\u0435\u043e\u0440\u0438\u044f. \u0412 \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435 \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u043f\u0440\u0435\u0434\u0438\u043c\u0441\u0442\u0432\u0430\u0442\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e, \u0432\u043a\u043b\u044e\u0447\u0432\u0430\u0439\u043a\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0437\u0430 \u0432\u0438\u0440\u0442\u0443\u0430\u043b\u043d\u0430 \u0440\u0435\u0430\u043b\u043d\u043e\u0441\u0442.<\/p>\n<p><em>Keywords:<\/em> education, virtual reality, virtual environment.<\/p>\n<p><strong>VIRTUAL REALITY \u2013 A NEW VISION&nbsp;<\/strong><strong>ON THE CONTEMPORARY EDUCATION<\/strong><\/p>\n<p><strong><br \/>Abstract.<\/strong> The paper considers basic concepts, ideas and principles of virtual reality technology. Some environments of virtual reality and their application are presented. Basic principles of teaching by means of virtual reality are described from educational point of view. Concluding advantages of education including virtual reality systems are pesented.<\/p>\n<p><strong>Daniela Minkovska<\/strong><br \/><em>Assist. Prof. Ph.D. <\/em><br \/><em>Department of Programming and Computer Technologies,<\/em><br \/><em>Faculty of Computer Systems and Management<\/em><br \/><em>Technical University of Sofia<\/em><\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<hr \/>\n<p><strong><a name=\"art06\">&nbsp;<\/a>\u0418\u0417\u041f\u041e\u041b\u0417\u0412\u0410\u041d\u0415 \u041d\u0410 \u0414\u0418\u041d\u0410\u041c\u0418\u0427\u041d\u0418 \u0418 <\/strong><strong>\u0418\u041d\u0422\u0415\u0420\u0410\u041a\u0422\u0418\u0412\u041d\u0418 \u041c\u041e\u0414\u0415\u041b\u0418 \u0417\u0410 \u041f\u0420\u0415\u0414\u0421\u0422\u0410\u0412\u042f\u041d\u0415 <br \/>\u041d\u0410 <\/strong><strong>\u0423\u0427\u0415\u0411\u041d\u041e\u0422\u041e \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u041f\u041e \u0414\u0418\u0421\u0426\u0418\u041f\u041b\u0418\u041d\u0410\u0422\u0410 <\/strong><strong>\u201e\u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420\u041d\u0418 \u041c\u0420\u0415\u0416\u0418 \u0418 \u041a\u041e\u041c\u0423\u041d\u0418\u041a\u0410\u0426\u0418\u0418\u201c<\/strong><\/p>\n<p><strong><br \/>Gencho Stoitsov<br \/>\u041a\u043e\u0441\u0442\u0430 \u0413\u044a\u0440\u043e\u0432<\/strong><\/p>\n<p><strong><br \/>Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u0438 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043e\u0431\u043e\u0433\u0430\u0442\u0435\u043d \u0441 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u043d\u0438 \u0438 \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u0438 \u043c\u043e\u0434\u0435\u043b\u0438 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u0430\u0440\u0438\u0443\u043c \u0437\u0430 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u043d\u0435 &nbsp;&nbsp;\u043d\u0430 \u0443\u0447\u0435\u0431\u043d\u043e \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u043f\u043e \u0434\u0438\u0441\u0446\u0438\u043f\u043b\u0438\u043d\u0430\u0442\u0430 \u201e\u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438 \u043c\u0440\u0435\u0436\u0438 \u0438 \u043a\u043e\u043c\u0443\u043d\u0438\u043a\u0430\u0446\u0438\u0438\u201c. \u041d\u0430\u043f\u0440\u0430\u0432\u0435\u043d \u0435 \u0430\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438 \u043e\u0442 \u043f\u0440\u043e\u0432\u0435\u0436\u0434\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u043e \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 \u0437\u0430 \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0430 \u043d\u0430 \u043f\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044f\u0442\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0430\u0432\u0430\u043d\u0438\u0442\u0435 \u0447\u0440\u0435\u0437 \u043e\u043d\u0430\u0433\u043b\u0435\u0434\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u043d\u043e\u0442\u043e \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u0441 \u0443\u0441\u043b\u043e\u0432\u043d\u043e \u0438\u0437\u043e\u0431\u0440\u0430\u0437\u0438\u0442\u0435\u043b\u043d\u0438 \u0438 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u043d\u0438 \u043c\u043e\u0434\u0435\u043b\u0438.<\/p>\n<p><em>Keywords:<\/em> networks, communications, training, dynamic visibility, communicative simulacrum, animation<\/p>\n<p><strong>USING DYNAMIC AND INTERACTIVE MODELS FOR CURRICULUM PRESENTATION&nbsp;<br \/><\/strong><strong>OF A \u201dCOMPUTER NETWORKS AND COMMUNICATIONS\u201c COURSE<\/strong><\/p>\n<p><strong><br \/>Abstract.<\/strong> The paper is dedicated to the elaboration and application of a methodological instrumentation that has been enriched by dynamic and interactive models to teach the curriculum of a \u201eComputer networks and communications\u201c course. A pedagogical investigation is carried out to check student performance. The theoretical content is visualized by conditionally expressive and dynamic models. The results are analyzed.<\/p>\n<p><strong>Gencho Stoitsov <\/strong><br \/><strong>Assistant professor<\/strong><br \/><em>Faculty of Mathematics and Informatics<\/em><br \/><em>Plovdiv University \u201ePaisii Hilendarski\u201c,<\/em><br \/><em>Plovdiv, Bulgaria<\/em><\/p>\n<p><strong>Kosta Garov<\/strong><br \/><strong>Associated professor, PhD<\/strong><br \/><em>Faculty of Mathematics and Informatics<\/em><br \/><em>Plovdiv University \u201ePaisii Hilendarski\u201c,<\/em><br \/><em>Plovdiv, Bulgaria<\/em><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: right;\"><em><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/em><\/p>\n<p style=\"text-align: right;\">&nbsp;<\/p>\n<hr \/>\n<p><em>&nbsp;<\/em><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: right;\"><em>&nbsp;<\/em><\/p>\n<p style=\"text-align: right;\"><em>&nbsp;<\/em><\/p>\n<p style=\"text-align: right;\"><em>&nbsp;<\/em><\/p>\n<p style=\"text-align: right;\"><em>&nbsp;<\/em><\/p>\n<p style=\"text-align: right;\"><em>&nbsp;<\/em><\/p>\n<p style=\"text-align: left;\"><em>&nbsp;<\/em><\/p>","protected":false},"excerpt":{"rendered":"<p>\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS 70-\u0433\u043e\u0434\u0438\u0448\u0435\u043d \u044e\u0431\u0438\u043b\u0435\u0439 \u2013 \u043f\u0440\u043e\u0444. \u0434\u043c\u043d \u0413\u0435\u043d\u0447\u043e \u0421\u043a\u043e\u0440\u0434\u0435\u0432 &#8211; \u0441\u0442\u0440. 9 &nbsp;\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \u0427\u0442\u043e \u0411\u043e\u043b\u044c\u0448\u043e\u0435: \u03c0% \u043e\u0442 e \u0438\u043b\u0438 e% \u043e\u0442 \u03c0? [What is Greater: \u03c0% of e or e% of \u03c0?] \/ \u041d. \u0420\u043e\u0437\u043e\u0432 \/ N. Rozov &#8211; \u0441\u0442\u0440. 17 &nbsp;\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432\u044a\u0440\u0445\u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0440\u0435\u0431\u0443\u0441\u0438 \u0438\u043b\u0438\u2026\u0415\u043c\u043f\u0438\u0440\u0438\u0447\u0435\u043d \u043f\u043e\u0434\u0445\u043e\u0434\u0437\u0430 \u043e\u0446\u0435\u043d\u043a\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":[2882],"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 LVI, 2013 - \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:\/\/history.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2013-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"&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 LVI, 2013 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS 70-\u0433\u043e\u0434\u0438\u0448\u0435\u043d \u044e\u0431\u0438\u043b\u0435\u0439 \u2013 \u043f\u0440\u043e\u0444. \u0434\u043c\u043d \u0413\u0435\u043d\u0447\u043e \u0421\u043a\u043e\u0440\u0434\u0435\u0432 &#8211; \u0441\u0442\u0440. 9 &nbsp;\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \u0427\u0442\u043e \u0411\u043e\u043b\u044c\u0448\u043e\u0435: \u03c0% \u043e\u0442 e \u0438\u043b\u0438 e% \u043e\u0442 \u03c0? 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