{"id":39268,"date":"2014-10-27T21:59:29","date_gmt":"2014-10-27T18:59:29","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lvi-2014\/"},"modified":"2019-06-24T17:33:15","modified_gmt":"2019-06-24T14:33:15","slug":"matematika-i-informatika-knizhka-5-godina-lvi-2014","status":"publish","type":"post","link":"https:\/\/vocedu.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lvi-2014\/","title":{"rendered":"Mathematics and Informatics, Number 5\/2014, Volume 57"},"content":{"rendered":"<p><strong><a name=\"top\">&nbsp;<\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 <\/strong><\/p>\n<p><strong>EDUCATIONAL TECHNOLOGIES \/&nbsp; \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418<\/strong> <\/p>\n<p><a href=\"#art01\">\u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u0448\u043a\u043e\u043b\u0430\u0445 \u0420\u043e\u0441\u0441\u0438\u0438 [Informatics in the Schools of Russia] \/ <\/a><br \/><em>\u0421. \u0410. \u0411\u0435\u0448\u0435\u043d\u043a\u043e\u0432, \u042d. \u0412. \u041c\u0438\u043d\u0434\u0437\u0430\u0435\u0432\u0430 \/ Sergei Beshenkov, Etery Mindzeva<\/em> &#8211; \u0441\u0442\u0440. 447<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art02\">\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043c\u043e\u0434\u0435\u043b\u0438 \u043d\u0430 \u0440\u0435\u0430\u043b\u043d\u0438 \u043f\u0440\u043e\u0446\u0435\u0441\u0438 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0438\u0442\u0435 \u0437\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0437\u0430 \u0442\u044f\u0445\u043d\u043e\u0442\u043e \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 [Mathematical Models of Real Processes and Applications of Computer Algebra Systems to Their Study] <\/a><br \/><em>\u0422\u0438\u0445\u043e\u043c\u0438\u0440 \u0418\u0432\u0430\u043d\u043e\u0432 \/ Tihomir Ivanov<\/em> \u2013 p. 462<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art03\">\u041e\u0449\u0435 \u0435\u0432\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u0441 Excel [More Heuristics by Excel] \/ <\/a><br \/><em>\u041f\u043b\u0430\u043c\u0435\u043d \u041f\u0435\u043d\u0435\u0432 \/ Plamen Penev<\/em> &#8211; \u0441\u0442\u0440. 472<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art04\">\u0418\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u0447\u043d\u0438\u044f \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0442\u043e\u0440 \u043d\u0430 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0441\u0445\u0435\u043c\u0438 LC \u043f\u0440\u0438 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043f\u044a\u043b\u043d\u0438 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u043e\u0442 \u0411\u0443\u043b\u0435\u0432\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 [Using the Graphic Constructor of Combinational Schemes LC in the Study of Complete Sets of Boolean Functions] \/ <\/a><br \/><em>\u0412\u0438\u043b\u0438\u0441\u043b\u0430\u0432 \u0420\u0430\u0434\u0435\u0432 \/ Vilislav Radev<\/em> &#8211; \u0441\u0442\u0440. 480<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/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=\"#art05\">\u0422\u0435\u043e\u0440\u0435\u0442\u0438\u043a\u043e-\u043c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0430\u0441\u043f\u0435\u043a\u0442\u044b \u043f\u0440\u043e\u0435\u043a\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f [Theoretical and Methodological Aspects of the Mathematics Education Concept Design] \/ <\/a><br \/><em>\u0413. \u0425. \u0413\u0430\u0439\u0434\u0430\u0440\u0436\u0438, \u0410. \u0410. \u0420\u0443\u0441\u0430\u043a\u043e\u0432\/ Georgi Gaidarji, Alexander Rusakov<\/em> &#8211; \u0441\u0442\u0440. 492<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art06\">\u0414\u0432\u0430 \u043f\u043e\u0434\u0445\u043e\u0434\u0430 \u0437\u0430 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \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 [Two Approaches to Study Equations in Primary School Mathematics] \/ <\/a><br \/><em>\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<\/em> &#8211; \u0441\u0442\u0440. 502<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art07\">\u041c\u0430\u0448\u0438\u043d\u0435\u043d \u043f\u043e\u0434\u0445\u043e\u0434 \u043a\u044a\u043c \u0415\u0432\u043a\u043b\u0438\u0434\u043e\u0432\u0430\u0442\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f: \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u043d\u0430 \u041e\u0439\u043b\u0435\u0440, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043d\u0430 \u041e\u0439\u043b\u0435\u0440 \u0438 \u0442\u0440\u0430\u043d\u0441\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u0438 \u043d\u0430 \u041e\u0439\u043b\u0435\u0440 [Machine Approach to Euclidean Geometry: Euler Triangles, Euler Products and Euler Transforms] \/ <\/a><br \/><em>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0414\u0435\u043a\u043e \u0414\u0435\u043a\u043e\u0432 \/ Sava Grozdev, Deko Dekov<\/em> &#8211; \u0441\u0442\u0440. 519<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/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>\u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f [Contest Problems of the Issue]&nbsp;&#8211; \u0441\u0442\u0440. 541<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/vocedu.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p>\u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u043e\u0442 \u0431\u0440\u043e\u0439 6, 2013 [Solutions of the Contest Problems from Issue 6, 2013] &#8211; \u0441\u0442\u0440. 542<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>READ IN THE LATEST ISSUES OF AZ BUKI JOURNALS \/ <\/strong><br \/><strong>\u0412 \u041d\u041e\u0412\u0418\u0422\u0415 \u0411\u0420\u041e\u0415\u0412\u0415 \u041d\u0410 \u0421\u041f\u0418\u0421\u0410\u041d\u0418\u042f\u0422\u0410 \u041d\u0410 \u0418\u0417\u0414\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u041e \u201e\u0410\u0417 \u0411\u0423\u041a\u0418\u201c \u0427\u0415\u0422\u0415\u0422\u0415<\/strong> &#8211; \u0441\u0442\u0440. 545<\/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> &#8211; \u0441\u0442\u0440. 547<\/p>\n<hr \/>\n<p><strong><a name=\"art01\">&nbsp;<\/a>\u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0422\u0418\u041a\u0410 \u0412 \u0428\u041a\u041e\u041b\u0410\u0425 \u0420\u041e\u0421\u0421\u0418\u0418 <\/strong><\/p>\n<p><strong>\u0421. \u0410. \u0411\u0435\u0448\u0435\u043d\u043a\u043e\u0432, \u042d. \u0412. \u041c\u0438\u043d\u0434\u0437\u0430\u0435\u0432\u0430<\/strong> <br \/><em>\u0418\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u044f \u0438 \u043c\u0435\u0442\u043e\u0434\u043e\u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0430\u044f \u0430\u043a\u0430\u0434\u0435\u043c\u0438\u044f \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f<\/em> <\/p>\n<p><strong>Abstract<\/strong>. \u0412 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0439 \u043e\u0431\u0449\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043a\u0443\u0440\u0441 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0438, \u0438 \u043a\u0430\u043a\u043e\u0432\u044b \u043f\u0435\u0440\u0441\u043f\u0435\u043a\u0442\u0438\u0432\u044b \u0435\u0433\u043e \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u044f \u0432 \u0420\u043e\u0441\u0441\u0438\u0438 \u0432 \u043f\u043b\u0430\u043d\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f. <\/p>\n<p><em>Keywords<\/em>: Informatics, curriculum, Computer science competency, general-educa- tional subject, meta-subject.<\/p>\n<p><strong>INFORMATICS IN THE SCHOOLS OF RUSSIA<\/strong><\/p>\n<p><strong>Abstract<\/strong>. The present paper considers the contemporary general-educational content of Informatics and the perspectives of its development in Russia in the context of solving the key problems of modern education. <\/p>\n<p><strong>Prof. Sergei Beshenkov, DSc,<\/strong><br \/><strong>Dr. Etery Mindzeva, Senior Researcher <\/strong><br \/>Laboratory on Didactics of Informatics <br \/>Institute for Content and Teaching Methods Russian Academy of Education <br \/>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=\"art02\">&nbsp;<\/a>\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u0418 \u041c\u041e\u0414\u0415\u041b\u0418 \u041d\u0410 \u0420\u0415\u0410\u041b\u041d\u0418 \u041f\u0420\u041e\u0426\u0415\u0421\u0418 \u0418 \u041f\u0420\u0418\u041b\u041e\u0416\u0415\u041d\u0418\u042f \u041d\u0410 \u0421\u0418\u0421\u0422\u0415\u041c\u0418\u0422\u0415&nbsp; \u0417\u0410 \u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420\u041d\u0410 \u0410\u041b\u0413\u0415\u0411\u0420\u0410&nbsp; \u0417\u0410 \u0422\u042f\u0425\u041d\u041e\u0422\u041e \u0418\u0417\u0421\u041b\u0415\u0414\u0412\u0410\u041d\u0415 <\/strong><\/p>\n<p><strong>\u0422\u0438\u0445\u043e\u043c\u0438\u0440 \u0418\u0432\u0430\u043d\u043e\u0432<\/strong> <br \/><em>Institute of Mathematics and Informatics \u2013 BAS<\/em><\/p>\n<p><strong>Abstract<\/strong>. \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0434\u0432\u0430 \u043f\u0440\u0438\u043b\u043e\u0436\u043d\u0438 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u043e\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u0442\u0430 \u043d\u0430 \u0435\u043a\u043e\u043b\u043e\u0433\u0438\u044f\u0442\u0430 \u0438 \u043e\u0442 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430\u0442\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0430. \u0426\u0435\u043b\u0442\u0430 \u0435 \u0434\u0430 \u0431\u044a\u0434\u0430\u0442 \u0434\u0430\u0434\u0435\u043d\u0438 \u043d\u044f\u043a\u043e\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0438, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0432\u0430\u0449\u0438 \u0434\u0430 \u0441\u0435 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0430\u0442 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0442\u0430 \u0437\u0430 \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0440\u0435\u0430\u043b\u043d\u0438 \u043f\u0440\u043e\u0446\u0435\u0441\u0438. \u041f\u043e\u043a\u0430\u0437\u0430\u043d\u043e \u0435 \u043a\u0430\u043a \u0441\u0438\u0441\u0442\u0435\u043c\u0438\u0442\u0435 \u0437\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0431\u044a\u0434\u0430\u0442 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0438 \u043a\u0430\u0442\u043e \u043c\u043d\u043e\u0433\u043e \u0443\u0434\u043e\u0431\u043d\u043e \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e \u0437\u0430 \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0437\u0430 \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u0440\u0435\u0441\u043c\u044f- \u0442\u0430\u043d\u0438\u044f, \u043f\u043e\u0440\u0430\u0434\u0438 \u043a\u043e\u0435\u0442\u043e \u0431\u0438 \u0431\u0438\u043b\u043e \u043f\u043e\u043b\u0435\u0437\u043d\u043e \u0434\u0430 \u043d\u0430\u043c\u0435\u0440\u044f\u0442 \u0441\u0432\u043e\u0435\u0442\u043e \u043c\u044f\u0441\u0442\u043e \u0432 \u0433\u0438\u043c\u043d\u0430\u0437\u0438\u0430\u043b\u043d\u043e\u0442\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u041f\u043e\u0434\u0447\u0435\u0440\u0442\u0430\u043d \u0435 \u043e\u0431\u0430\u0447\u0435 \u0444\u0430\u043a\u0442\u044a\u0442, \u0447\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u044f\u0442 \u0441\u043e\u0444\u0442\u0443\u0435\u0440 \u043d\u0435 \u0431\u0438\u0432\u0430 \u0434\u0430 \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 \u043a\u0430\u0442\u043e \u0437\u0430\u043c\u0435\u0441\u0442\u0438\u0442\u0435\u043b, \u0430 \u043a\u0430\u0442\u043e \u0434\u043e\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435 \u043a\u044a\u043c \u201e\u043a\u043b\u0430\u0441\u0438\u0447\u0435\u0441\u043a\u0430\u0442\u0430\u201c \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. <\/p>\n<p><em>Keywords<\/em>: mathematical modeling, computer algebra systems, education<\/p>\n<p><strong>MATHEMATICAL MODELS OF REAL PROCESSES AND APPLICATIONS OF COMPUTER ALGEBRA SYSTEMS TO THEIR STUDY<\/strong><\/p>\n<p><strong>Abstract.<\/strong> In this paper, we present two applied problems\u2014from the fields of ecology and computer graphics. Our goal is to give some examples that can be used to show applications of mathematics for modeling real processes. Also, we show that computer algebra systems can be used as an invaluable tool for visualization and for technical calculations and, thus, they should find their place in high school education in mathematics. We emphasize the fact that mathematical software, however, should not be treated as a substitution, but as an addition to \u201cclassical\u201d math training. <\/p>\n<p><strong>Mr. Tihomir Ivanov<\/strong> <br \/>Institute of Mathematics and Informatics <br \/>Bulgarian Academy of Sciences<\/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=\"art03\">&nbsp;<\/a>\u041e\u0429\u0415 \u0415\u0412\u0420\u0418\u0421\u0422\u0418\u041a\u0418 \u0421 EXCEL<\/strong><\/p>\n<p><strong>Plamen Penev<\/strong> <br \/><em>\u0421\u041e\u0423 \u201e\u041f. \u0412\u043e\u043b\u043e\u0432\u201c \u2013 \u0428\u0443\u043c\u0435\u043d<\/em><\/p>\n<p><strong>Abstract<\/strong>. \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0438\u0440\u0430 \u0437\u0430 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435\u0442\u043e \u043d\u0430&nbsp; \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430\u0442\u0430 \u0441\u0440\u0435\u0434\u0430 \u043d\u0430 Excel, \u043e\u043f\u0438\u0441\u0430\u043d\u0430 \u0432 \u0431\u0440. 1 \u043e\u0442 2014 \u0433. \u043d\u0430 \u201e\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u201c. \u041e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u0432\u0430 \u0441\u0435 \u043e\u0442\u043a\u0440\u0438\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0440\u0443\u0431\u0440\u0438\u043a\u0430 \u201e\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0441 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u201c. <\/p>\n<p><em>Keywords<\/em>: problem solving, equation, numbers, tables, macros<\/p>\n<p><strong>MORE HEURISTICS BY EXCEL<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The paper informs about the development of the experimental platform of Excel, described in issue 1, 2014 of \u201cMathematics and Informatics\u201d journal. Reasons are given for the start of the new heading \u201cMathematics with computer\u201d in the journal. &nbsp;<\/p>\n<p><strong>Mr. Plamen Penev<\/strong> <br \/>Teacher in Informatics <br \/>Secondary school \u201cP. Volov\u201d<\/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=\"art04\">&nbsp;<\/a>\u0418\u0417\u041f\u041e\u041b\u0417\u0412\u0410\u041d\u0415 \u041d\u0410 \u0413\u0420\u0410\u0424\u0418\u0427\u041d\u0418\u042f \u041a\u041e\u041d\u0421\u0422\u0420\u0423\u041a\u0422\u041e\u0420 \u041d\u0410 \u041a\u041e\u041c\u0411\u0418\u041d\u0410\u0426\u0418\u041e\u041d\u041d\u0418 \u0421\u0425\u0415\u041c\u0418 LC \u041f\u0420\u0418&nbsp; \u0418\u0417\u0423\u0427\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u041f\u042a\u041b\u041d\u0418 \u041c\u041d\u041e\u0416\u0415\u0421\u0422\u0412\u0410&nbsp; \u041e\u0422 \u0411\u0423\u041b\u0415\u0412\u0418 \u0424\u0423\u041d\u041a\u0426\u0418\u0418 <\/strong><\/p>\n<p><strong>Vilislav Radev<\/strong> <br \/><em>University of Plovdiv \u201cPaisii Hilendarski\u201d<\/em><\/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 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u0447\u043d\u0438\u044f \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0442\u043e\u0440 \u043d\u0430 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0441\u0445\u0435\u043c\u0438 LC \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u041a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0442\u043e\u0440\u044a\u0442 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0432\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0432\u0430\u0449\u0430 \u0433\u0440\u0430\u0444\u0438\u0447\u043d\u043e \u0438\u043b\u0438 \u0442\u0430\u0431\u043b\u0438\u0447\u043d\u043e \u0437\u0430\u0434\u0430\u0432\u0430\u043d\u0435, \u0438\u0437\u0447\u0435\u0440\u0442\u0430\u0432\u0430\u043d\u0435 \u0438 \u0438\u0437\u0447\u0438\u0441\u043b\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0441\u0445\u0435\u043c\u0438 \u0437\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435 \u043d\u0430 \u0431\u0443\u043b\u0435\u0432\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0421 \u043d\u0435\u0433\u043e\u0432\u0430 \u043f\u043e\u043c\u043e\u0449 \u0435 \u0441\u044a\u0437\u0434\u0430\u0434\u0435\u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u0437\u0430 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043f\u044a\u043b\u043d\u0438 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u0432 \u0435\u0434\u0438\u043d \u043a\u043b\u0430\u0441\u0438\u0447\u0435\u0441\u043a\u0438 \u0440\u0430\u0437\u0434\u0435\u043b \u043e\u0442 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u0430\u0442\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043a\u0430\u043a\u0432\u0430\u0442\u043e \u0435 \u0442\u0435\u043e\u0440\u0438\u044f\u0442\u0430 \u043d\u0430 \u0431\u0443\u043b\u0435\u0432\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u0435 \u043f\u0440\u0435\u0434\u043d\u0430\u0437\u043d\u0430\u0447\u0435\u043d\u0430 \u0437\u0430 \u0443\u0447\u0438\u0442\u0435\u043b\u0438 \u0438 \u0443\u043d\u0438\u0432\u0435\u0440- \u0441\u0438\u0442\u0435\u0442\u0441\u043a\u0438 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u0442\u0435\u043b\u0438, \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u0449\u0438 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. <\/p>\n<p><em>Keywords<\/em>: logic circuits, boolean functions, graphic user interface<\/p>\n<p><strong>USING THE GRAPHIC CONSTRUCTOR OF COMBINATIONAL SCHEMES LC IN THE STUDY&nbsp; OF COMPLETE SETS OF BOOLEAN FUNCTIONS <\/strong><\/p>\n<p><strong>Abstract.<\/strong> The paper considers the use of the graphic constructor of combinational schemes LC in Discrete mathematics teaching. The constructor is a program system, which helps graphics or table determination, drawing and computation of combinational schemes in Boolean functions representations. An exemplary working out is created by it to teach complete sets in a classic chapter of Discrete mathematics like the theory of Boolean functions. The paper is addressed to secondary school teachers and university lecturers, who&nbsp; teach Discrete mathematics. <\/p>\n<p><strong>Mr. Vilislav Radev<\/strong> <br \/>Faculty of Mathematics and Informatics, <br \/>University of Plovdiv<\/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=\"art05\">&nbsp;<\/a>\u0422\u0415\u041e\u0420\u0415\u0422\u0418\u041a\u041e-\u041c\u0415\u0422\u041e\u0414\u041e\u041b\u041e\u0413\u0418\u0427\u0415\u0421\u041a\u0418\u0415 \u0410\u0421\u041f\u0415\u041a\u0422\u042b \u041f\u0420\u041e\u0415\u041a\u0422\u0418\u0420\u041e\u0412\u0410\u041d\u0418\u042f \u041a\u041e\u041d\u0426\u0415\u041f\u0426\u0418\u0418&nbsp; \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u041e\u0413\u041e \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u042f<\/strong><\/p>\n<p><strong>1\u0413. \u0425. \u0413\u0430\u0439\u0434\u0430\u0440\u0436\u0438,&nbsp; 2\u0410. \u0410. \u0420\u0443\u0441\u0430\u043a\u043e\u0432 <\/strong><br \/><em>1\u041f\u0413\u0423 \u0438\u043c. \u0422. \u0413. \u0428\u0435\u0432\u0447\u0435\u043d\u043a\u043e <\/em><br \/><em>2\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 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u043f\u0440\u0438\u0431\u043e\u0440\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0438<\/em><\/p>\n<p><strong>Abstract<\/strong>. \u0412 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043e\u0431\u0441\u0443\u0436\u0434\u0430\u0435\u0442\u0441\u044f \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u041f\u0440\u0438\u0434\u043d\u0435\u0441\u0442\u0440\u043e\u0432\u0441\u043a\u043e\u0439 \u043c\u043e\u043b\u0434\u0430\u0432\u0441\u043a\u043e\u0439 \u0440\u0435\u0441\u043f\u0443\u0431\u043b\u0438\u043a\u0438 (\u041f\u041c\u0420). <\/p>\n<p><em>Keywords<\/em>: Mathematics, mathematical competency, general-educational curriculum.<\/p>\n<p><strong>THEORETICAL-METHODOLOGICAL ASPECTS OF THE MATHEMATICS EDUCATION CONCEPT DESIGN <\/strong><\/p>\n<p><strong>Abstract<\/strong>. The paper considers the Mathematical education concept design on the example of the Pridnestrovian Moldavian Republic. <\/p>\n<p><strong>Prof. Dr. Georgi Gaidarji<\/strong> <br \/>Laboratory on Didactics of Mathematics <br \/>Pridnestrovian State University <br \/>Tiraspol, Pridnestrovian Moldavian Republic <\/p>\n<p><strong>Prof. Dr. Alexander Rusakov&nbsp;<\/strong><\/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=\"art06\">&nbsp;<\/a>\u0414\u0412\u0410 \u041f\u041e\u0414\u0425\u041e\u0414\u0410 \u0417\u0410 \u0418\u0417\u0423\u0427\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u0423\u0420\u0410\u0412\u041d\u0415\u041d\u0418\u042f \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><strong>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, 3\u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430<\/strong> <br \/><em>1\u0421\u043e\u0444\u0438\u0439\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u201e\u0421\u0432. \u041a\u043b\u0438\u043c\u0435\u043d\u0442 \u041e\u0445\u0440\u0438\u0434\u0441\u043a\u0438\u201c <\/em><br \/><em>2\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 \u201e\u0421\u0432. \u0441\u0432. \u041a\u0438\u0440\u0438\u043b \u0438 \u041c\u0435\u0442\u043e\u0434\u0438\u0439\u201c <\/em><br \/><em>3\u0421\u043e\u0444\u0438\u0439\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u201e\u0421\u0432. \u041a\u043b\u0438\u043c\u0435\u043d\u0442 \u041e\u0445\u0440\u0438\u0434\u0441\u043a\u0438\u201c<\/em><\/p>\n<p><strong>Abstract<\/strong>. \u0410\u0432\u0442\u043e\u0440\u0438\u0442\u0435 \u0432\u044a\u0432\u0435\u0436\u0434\u0430\u0442 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438 \u043f\u0440\u0430\u0432\u044f\u0442 \u043c\u0430- \u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0438 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u0430\u0440\u0430\u043b\u0435\u043b \u043c\u0435\u0436\u0434\u0443 \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u043e\u043d\u043d\u0438\u044f \u043c\u0435\u0442\u043e\u0434 \u043d\u0430 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0438\u044f \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442 \u0438 \u043c\u0435\u0442\u043e\u0434\u0430 \u043d\u0430 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438\u0442\u0435 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0432\u0430\u043d\u0438\u044f (\u0438\u043d\u0432\u0435\u0440\u0441\u0438\u044f\u0442\u0430) \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \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. <\/p>\n<p><em>Keywords<\/em>: primary school mathematics, arithmetical equation, arithmetical transfor- mation, inversion, mathematical model<\/p>\n<p><strong>TWO APPROACHES TO STUDY EQUATIONS IN PRIMARY SCHOOL MATHEMATICS<\/strong><\/p>\n<p><strong>Abstract.<\/strong> The authors initiate the idea of arithmetical equation and draw a mathematical and didactical parallel between the traditional method of the unknown component and the method of arithmetical transformations (the inversion method) for solving arithmetical equations in primary school mathematics.<\/p>\n<p><strong>Prof. Dr. Zdravko<\/strong> <br \/>Lalchev Faculty of Preschool and Primary Education <br \/>University of Sofia<\/p>\n<p><strong>Prof. Dr. Margarita Varbanova<\/strong> <br \/>Faculty of Mathematics and Informatics <br \/>University of VelikoTarnovo<\/p>\n<p><strong>Dr. Irina Voutova, Assist. Prof.<\/strong> <br \/>Faculty of Mathematics and Informatics <br \/>University of Sofia<\/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=\"art07\">&nbsp;<\/a>\u041c\u0410\u0428\u0418\u041d\u0415\u041d \u041f\u041e\u0414\u0425\u041e\u0414 \u041a\u042a\u041c \u0415\u0412\u041a\u041b\u0418\u0414\u041e\u0412\u0410\u0422\u0410 \u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u042f: \u0422\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u0426\u0418 \u041d\u0410 \u041e\u0419\u041b\u0415\u0420,&nbsp; \u041f\u0420\u041e\u0418\u0417\u0412\u0415\u0414\u0415\u041d\u0418\u042f \u041d\u0410 \u041e\u0419\u041b\u0415\u0420&nbsp; \u0418 \u0422\u0420\u0410\u041d\u0421\u0424\u041e\u0420\u041c\u0410\u0426\u0418\u0418 \u041d\u0410 \u041e\u0419\u041b\u0415\u0420 <\/strong><\/p>\n<p><strong>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432,&nbsp; \u0414\u0435\u043a\u043e \u0414\u0435\u043a\u043e\u0432<\/strong> <br \/><em>Institute of Mathematics and Informatics \u2013 BAS<\/em><\/p>\n<p><strong>Abstract<\/strong>. \u0410\u0432\u0442\u043e\u0440\u0438\u0442\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u0442 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438 \u0437\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043d\u0430 \u041e\u0439\u043b\u0435\u0440 \u0438 \u0442\u0440\u0430\u043d\u0441\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u0438 \u043d\u0430 \u041e\u0439\u043b\u0435\u0440. \u0420\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u0441\u0430 \u043e\u0442\u043a\u0440\u0438\u0442\u0438 \u043e\u0442 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430\u0442\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u201e\u041e\u0442\u043a\u0440\u0438\u0432\u0430\u0442\u0435\u043b\u201c. <\/p>\n<p><em>Keywords<\/em>: computer-generated mathematics, Euler triangle, Euler product, Euler transform, Euclidean geometry, Discoverer<\/p>\n<p><strong>MACHINE APPROACH TO EUCLIDEAN GEOMETRY: EULER TRIANGLES, EULER PRODUCTS AND EULER TRANSFORMS<\/strong><\/p>\n<p><strong>Abstract<\/strong>. The authors present some results concerning Euler products and Euler transforms. The results are discovered by the computer program \u201cDiscoverer\u201d.<\/p>\n<p><strong>Prof. Sava Grozdev, DSc<\/strong> <br \/>Institute of Mathematics and Informatics \u2013 BAS<\/p>\n<p>Dr. Deko Dekov, Assoc. Prof.<\/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=\"art08\">&nbsp;<\/a>\u0424\u041e\u0420\u041c\u0418\u0420\u0410\u041d\u0415 \u041d\u0410 \u0417\u041d\u0410\u041d\u0418\u042f \u0412\u042a\u0420\u0425\u0423 \u041a\u0420\u0418\u0412\u0418\u0422\u0415 \u041e\u0422 \u0412\u0422\u041e\u0420\u0410 \u0421\u0422\u0415\u041f\u0415\u041d <\/strong><\/p>\n<p><strong>1\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, 2\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<\/strong> <br \/><em>1\u0418\u043d\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 \u2013 \u0411\u0410\u041d <\/em><br \/><em>2\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u041b\u043e\u0432\u0435\u0447<\/em> <\/p>\n<p><strong>Abstract<\/strong>. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u043a\u0440\u0438\u0432\u0438 \u043e\u0442 \u0432\u0442\u043e\u0440\u0430 \u0441\u0442\u0435\u043f\u0435\u043d \u043a\u0430\u0442\u043e \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u0438 \u043e\u0431\u043e\u0431- \u0449\u0435\u043d\u0438\u044f \u043d\u0430 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435. \u0426\u0435\u043b\u0442\u0430 \u0435 \u0444\u043e\u0440\u043c\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0437\u043d\u0430\u043d\u0438\u044f, \u043e\u0441\u0438\u0433\u0443\u0440\u044f\u0432\u0430\u0449\u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442 \u0437\u0430 \u043e\u0431\u043e\u0431\u0449\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u0415\u0432\u043a\u043b\u0438\u0434\u043e\u0432\u0430\u0442\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f. <\/p>\n<p><em>\u041a\u0435\u0443words<\/em>: circle, Apollonius circle, ellipse, parabola, hyperbola, conic&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n<p><strong>FORMATION OF KNOWLEDGE ON CURVES OF SECOND DEGREE <\/strong><\/p>\n<p><strong>Abstract<\/strong>. Curves of second degree are considered in the paper as natural generalizations of circles. The aim is to form knowledge giving possibility of generalizing problems from Euclidean Geometry. &nbsp;<\/p>\n<p><strong>Prof. Sava Grozdev, DSc<\/strong> <br \/>Institute of Mathematics and Informatics \u2013 BAS<\/p>\n<p><strong>Dr. Veselin Nenkov, Assoc. Prof.<\/strong> <br \/>Technical College Lovech<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p>&nbsp;<\/p>","protected":false},"excerpt":{"rendered":"<p>&nbsp;CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 EDUCATIONAL TECHNOLOGIES \/&nbsp; \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418 \u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u0448\u043a\u043e\u043b\u0430\u0445 \u0420\u043e\u0441\u0441\u0438\u0438 [Informatics in the Schools of Russia] \/ \u0421. \u0410. \u0411\u0435\u0448\u0435\u043d\u043a\u043e\u0432, \u042d. \u0412. \u041c\u0438\u043d\u0434\u0437\u0430\u0435\u0432\u0430 \/ Sergei Beshenkov, Etery Mindzeva &#8211; \u0441\u0442\u0440. 447 &nbsp; &nbsp; \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043c\u043e\u0434\u0435\u043b\u0438 \u043d\u0430 \u0440\u0435\u0430\u043b\u043d\u0438 \u043f\u0440\u043e\u0446\u0435\u0441\u0438 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0438\u0442\u0435 \u0437\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0437\u0430 \u0442\u044f\u0445\u043d\u043e\u0442\u043e \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0435 [Mathematical Models of Real Processes [&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 5, \u0433\u043e\u0434\u0438\u043d\u0430 LVII, 2014 - \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:\/\/science.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-5-godina-lvi-2014\/\" \/>\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 5, \u0433\u043e\u0434\u0438\u043d\u0430 LVII, 2014 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"&nbsp;CONTENTS \/ 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