{"id":39330,"date":"2014-11-27T21:59:29","date_gmt":"2014-11-27T18:59:29","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-6-godina-lvi-2014\/"},"modified":"2019-06-24T17:33:15","modified_gmt":"2019-06-24T14:33:15","slug":"matematika-i-informatika-knizhka-6-godina-lvi-2014","status":"publish","type":"post","link":"https:\/\/science.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-6-godina-lvi-2014\/","title":{"rendered":"Mathematics and Informatics, Number 6\/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 \/ \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\">\u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430: \u0431\u0435\u043b\u0435\u0436\u043a\u0430 \u0437\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 \u043d\u0430 \u0425\u0430\u0438\u043c\u043e\u0432 [Computer-Generated Mathematics: a Note on the Haimov Triangle] \/ <\/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. 559<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>[\/emember_protected]<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/science.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=\"#art04\">A Refinement of an Inequality with Radicals \/ <\/a><br \/><em>\u0160efket Arslangi\u0107<\/em> &#8211; \u0441\u0442\u0440. 597<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art05\">An Inequality for Right Triangle and Its Generalization \/<\/a><br \/> <em>\u0160efket Arslangi\u0107<\/em> &#8211; \u0441\u0442\u0440. 604<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art06\">\u041a\u043e\u043d\u043a\u0443\u0440\u0435\u043d\u0442\u043d\u043e\u0441\u0442, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0430 \u043e\u0442 \u0442\u0430\u043d\u0433\u0435\u043d\u0442\u0438 [A Concurrence, Generated by Tangents] \/ <\/a><br \/><em>\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<\/em> \u2013 p. 603<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>[\/emember_protected]<\/p>\n<p><a href=\"#art07\">\u041f\u0435\u0434\u0430\u043b\u043d\u0430 \u043a\u0440\u0438\u0432\u0430 \u043d\u0430 \u0442\u043e\u0447\u043a\u0430 \u0441\u043f\u0440\u044f\u043c\u043e \u0424\u043e\u0439\u0435\u0440\u0431\u0430\u0445\u043e\u0432\u0430 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u044f [A Pedal Curve of a Point with Respect to a Feuerbach Configuration] \/ <\/a><br \/><em>\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<\/em> &#8211; \u0441\u0442\u0440. 617<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><a href=\"#art08\">\u0415\u0432\u0440\u043e\u043f\u0435\u0439\u0441\u043a\u0438 \u0438\u0437\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u0441\u043a\u0438 \u0433\u0440\u0443\u043f\u0438 \u0441 \u0438\u043d\u0434\u0443\u0441\u0442\u0440\u0438\u044f\u0442\u0430 \u2013 \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u0438 \u0438 \u043f\u0435\u0440\u0441\u043f\u0435\u043a\u0442\u0438\u0432\u0438 [European Study Group with Industry \u2013 Traditions and Challenges] \/ <\/a><br \/><em>\u0421\u0442\u0435\u0444\u043a\u0430 \u0414\u0438\u043c\u043e\u0432\u0430 \/ Stefka Dimova<\/em> &#8211; \u0441\u0442\u0440. 626<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><strong>CONTEST PROBLEMS \/&nbsp; \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] &#8211; \u0441\u0442\u0440. 633<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">&nbsp;<a href=\"https:\/\/science.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 1, 2014 [Solutions of the Contest Problems from Issue 1, 2014] &#8211; \u0441\u0442\u0440. 634<\/p>\n<p><strong>ANNUAL CONTENTS \/ \u0413\u041e\u0414\u0418\u0428\u041d\u041e \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong> &#8211; \u0441\u0442\u0440. 636<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a><\/p>\n<p><strong>READ IN THE LATEST ISSUES OF \u201eAZ BUKI\u201c 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&nbsp; \u201e\u0410\u0417 \u0411\u0423\u041a\u0418\u201c \u0427\u0415\u0422\u0415\u0422\u0415<\/strong> &#8211; \u0441\u0442\u0440. 641<\/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. 643<\/p>\n<hr \/>\n<p><strong><a name=\"art01\">&nbsp;<\/a>\u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420\u041d\u041e \u0413\u0415\u041d\u0415\u0420\u0418\u0420\u0410\u041d\u0410 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410:&nbsp; \u0411\u0415\u041b\u0415\u0416\u041a\u0410 \u0417\u0410 \u0422\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u041a\u0410 \u041d\u0410 \u0425\u0410\u0418\u041c\u041e\u0412<\/strong><\/p>\n<p><strong>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \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>.&nbsp; \u0412 \u0442\u0430\u0437\u0438 \u0431\u0435\u043b\u0435\u0436\u043a\u0430 \u0430\u0432\u0442\u043e\u0440\u0438\u0442\u0435 \u0434\u0430\u0432\u0430\u0442 \u043d\u044f\u043a\u043e\u0438 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438, \u043e\u0442\u043d\u0430\u0441\u044f\u0449\u0438 \u0441\u0435 \u0434\u043e \u0442\u0440\u0438\u044a\u0433\u044a\u043b- \u043d\u0438\u043a\u0430 \u043d\u0430 \u0425\u0430\u0438\u043c\u043e\u0432. \u0420\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u0441\u0430 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\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, Euclidean geometry, \u201cDiscoverer\u201d, Haimov triangle<\/p>\n<p><strong>COMPUTER-GENERATED MATHEMATICS: A NOTE ON THE HAIMOV TRIANGLE<\/strong><\/p>\n<p><strong>Abstract.<\/strong> In this note the authors present some results related to the Haimov triangle. The results are generated 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><strong>Dr. Deko Dekov, Assoc. Prof.<\/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=\"art02\">&nbsp;<\/a>\u0423\u0427\u0415\u041d\u0415 \u0427\u0420\u0415\u0417 \u041e\u0422\u041a\u0420\u0418\u0422\u0418\u042f \u2013&nbsp; \u041d\u041e\u0412 \u0415\u0424\u0415\u041a\u0422\u0418\u0412\u0415\u041d \u041f\u041e\u0414\u0425\u041e\u0414 \u0412 \u0423\u0427\u0415\u041d\u0415\u0422\u041e&nbsp; \u0427\u0420\u0415\u0417 \u0415\u041a\u0421\u041f\u0415\u0420\u0418\u041c\u0415\u041d\u0422\u0418\u0420\u0410\u041d\u0415 <\/strong><\/p>\n<p><strong>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \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>. \u041f\u0440\u0435\u0437 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0442\u0435 \u0433\u043e\u0434\u0438\u043d\u0438 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0438\u044f\u0442 \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e, \u0438\u0437\u0432\u0435\u0441\u0442\u0435\u043d \u043a\u0430\u0442\u043e \u201e\u0443\u0447\u0435\u043d\u0435 \u0447\u0440\u0435\u0437 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u0435\u201c \u0438\u043b\u0438 \u201e\u0443\u0447\u0435\u043d\u0435 \u0447\u0440\u0435\u0437 \u043f\u0440\u0435\u043e\u0442\u043a\u0440\u0438\u0442\u0438\u044f\u201c \u0438 \u043d\u0435- \u043f\u0440\u0430\u0432\u0438\u043b\u043d\u043e \u043d\u0430\u0440\u0438\u0447\u0430\u043d \u201e\u0438\u0437\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u0441\u043a\u0438 \u043f\u043e\u0434\u0445\u043e\u0434\u201c, \u0441\u0442\u0430\u0432\u0430 \u0432\u0441\u0435 \u043f\u043e-\u043f\u043e\u043f\u0443\u043b\u044f\u0440\u0435\u043d. \u0412\u0430\u0436\u043d\u043e \u0435 \u0434\u0430 \u0441\u0435 \u043e\u0442\u0431\u0435\u043b\u0435\u0436\u0438, \u0447\u0435 \u043f\u0440\u0438 \u0443\u0447\u0435\u043d\u0435\u0442\u043e \u0447\u0440\u0435\u0437 \u043f\u0440\u0435\u043e\u0442\u043a\u0440\u0438\u0442\u0438\u044f \u0432 \u0445\u043e\u0434\u0430 \u043d\u0430 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0438\u044f \u043f\u0440\u043e\u0446\u0435\u0441 \u0443\u0447\u0435\u043d\u0438\u043a\u044a\u0442 \u0438\u043b\u0438 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u044a\u0442 \u043f\u043e\u043b\u0443\u0447\u0430\u0432\u0430 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0438 \u0437\u0430 \u043d\u0435\u0433\u043e \u0444\u0430\u043a\u0442\u0438, \u043a\u043e\u0438\u0442\u043e \u0432 \u043e\u0442\u0434\u0435\u043b\u043d\u0438 \u0441\u043b\u0443\u0447\u0430\u0438 \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0441\u0435 \u043e\u043a\u0430\u0436\u0430\u0442 \u043d\u043e\u0432\u0438 \u043d\u0430\u0443\u0447\u043d\u0438 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438. \u041f\u043e\u043b\u0443\u0447\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043d\u043e\u0432 \u043d\u0430\u0443\u0447\u0435\u043d \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442 \u0435 \u0441\u044a\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043e \u0438 \u0442\u043e \u043c\u043e\u0436\u0435 \u0434\u0430 \u0431\u044a\u0434\u0435 \u043f\u043e\u0441\u0442\u0430\u0432\u0435\u043d\u043e \u043a\u0430\u0442\u043e \u0446\u0435\u043b \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e. \u0412 \u0442\u043e\u0437\u0438 \u0441\u043b\u0443\u0447\u0430\u0439 \u0435 \u043f\u043e\u0434\u0445\u043e\u0434\u044f\u0449\u043e \u0441\u044a\u043e\u0442\u0432\u0435\u0442\u043d\u043e\u0442\u043e \u0443\u0447\u0435\u043d\u0435 \u0434\u0430 \u0441\u0435 \u043d\u0430\u0440\u0438\u0447\u0430 \u201e\u0443\u0447\u0435\u043d\u0435 \u0447\u0440\u0435\u0437 \u043e\u0442\u043a\u0440\u0438\u0442\u0438\u044f\u201c. \u041f\u043e \u0442\u043e\u0437\u0438 \u043d\u0430\u0447\u0438\u043d \u0432 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0438\u044f \u043f\u043e\u0434\u0445\u043e\u0434, \u0442.\u0435. \u0432 \u0443\u0447\u0435\u043d\u0435\u0442\u043e \u0447\u0440\u0435\u0437 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u0435, \u0441\u0435 \u043e\u0444\u043e\u0440\u043c\u044f\u0442 \u0434\u0432\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f: \u0443\u0447\u0435\u043d\u0435 \u0447\u0440\u0435\u0437 \u043f\u0440\u0435\u043e\u0442\u043a\u0440\u0438\u0442\u0438\u044f \u0438 \u0443\u0447\u0435\u043d\u0435 \u0447\u0440\u0435\u0437 \u043e\u0442\u043a\u0440\u0438\u0442\u0438\u044f. \u0422\u043e\u0447\u043d\u043e \u0443\u0447\u0435\u043d\u0435\u0442\u043e \u0447\u0440\u0435\u0437 \u043e\u0442\u043a\u0440\u0438\u0442\u0438\u044f, \u0430 \u043d\u0435 \u0443\u0447\u0435\u043d\u0435\u0442\u043e \u0447\u0440\u0435\u0437 \u043f\u0440\u0435\u043e\u0442\u043a\u0440\u0438\u0442\u0438\u044f, \u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043d\u043e \u0434\u0430 \u0441\u0435 \u043d\u0430\u0440\u0438\u0447\u0430 \u0438\u0437\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u0441\u043a\u0438 \u043f\u043e\u0434\u0445\u043e\u0434. \u041d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u0438\u043c\u0435\u043d\u043d\u043e \u043d\u0430 \u043f\u043e\u0434\u0445\u043e\u0434\u0430 \u0437\u0430 \u0443\u0447\u0435\u043d\u0435 \u0447\u0440\u0435\u0437 \u043e\u0442\u043a\u0440\u0438\u0442\u0438\u044f. \u0410\u0432\u0442\u043e\u0440\u0438\u0442\u0435 \u043f\u0440\u0438\u0432\u0435\u0436\u0434\u0430\u0442 \u043f\u0440\u0438\u043c\u0435\u0440\u0438, \u043f\u043e\u043a\u0430\u0437\u0432\u0430\u0449\u0438 \u043a\u0430\u043a \u043c\u043e\u0436\u0435 \u0434\u0430 \u0431\u044a\u0434\u0435 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u043d\u0438\u044f\u0442 \u043f\u043e\u0434\u0445\u043e\u0434. <\/p>\n<p><em>Keywords<\/em>: learning through discoveries, learning through rediscoveries, research approach in education, experimental approach in education, computer-generated mathematics, Euclidean geometry, \u201cDiscoverer\u201d.<\/p>\n<p><strong>LEARNING THROUGH DISCOVERIES \u2013 A NEW EFFECTIVE APPROACH WITHIN LEARNING THROUGH EXPERIMENTATION<\/strong><\/p>\n<p><strong>Abstract.<\/strong> Recently the experimental approach in education, known as \u201clearning through experimentation\u201d or \u201clearning through rediscoveries\u201d and incorrectly called to be \u201cresearch approach\u201d, becomes more popular. It is important to note, that in learning through rediscoveries during the experimentation process the student obtains unknown to him\/her facts, which could turn out to be new scientific results in some cases.&nbsp; It is essential to obtain a new scientific result and this could be put as a goal in education. In this case it is convenient to call the coresponding learning to be \u201elearning through discoveries\u201c. In such a way two directions are formed in the experimental approach, i.e. in learning through ecperimentation: learning through rediscoveries and learning through discoveries. It is correct, that exactly learning throgh discoveries&nbsp; should be called to be reaserch approach and not learning through rediscoveries. Namely, the present paper is dedicated to learning through discoveries. The authors discuss some examples how the proposed approach could be applied. &nbsp;<\/p>\n<p><strong>Prof. Sava Grozdev, DSc.<\/strong> <br \/>Institute of Mathematics and Informatics \u2013 BAS<\/p>\n<p><strong>Dr. Deko Dekov, Assoc. Prof.<\/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=\"art03\">&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 <\/strong><br \/><strong>\u0417\u0410 \u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420\u041d\u0410 \u0410\u041b\u0413\u0415\u0411\u0420\u0410 \u0417\u0410 \u0422\u042f\u0425\u041d\u041e\u0422\u041e \u0418\u0417\u0421\u041b\u0415\u0414\u0412\u0410\u041d\u0415 \u0427\u0430\u0441\u0442 \u0432\u0442\u043e\u0440\u0430 <\/strong><\/p>\n<p><strong>\u0422\u0438\u0445\u043e\u043c\u0438\u0440 \u0418\u0432\u0430\u043d\u043e\u0432<\/strong> <br \/><em>Sofia University <\/em><br \/><em>Institute of Mathematics and Informatics \u2013 BAS<\/em><\/p>\n<p><strong>Abstract<\/strong>. \u041d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u043f\u0440\u043e\u0434\u044a\u043b\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u0442\u0435\u043c\u0430\u0442\u0430, \u0437\u0430\u043f\u043e\u0447\u043d\u0430\u0442\u0430 \u0432 \u0431\u0440. 5\/2014 \u043d\u0430 \u0441\u043f. \u201e\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u201c. \u0421\u0442\u044a\u043f\u0432\u0430\u0439\u043a\u0438 \u043d\u0430 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u0438\u044f \u043b\u043e\u0433\u0438\u0441\u0442\u0438\u0447\u0435\u043d \u043c\u043e\u0434\u0435\u043b, \u0437\u0430 \u043a\u043e\u0439\u0442\u043e \u0433\u043e\u0432\u043e\u0440\u0438\u0445\u043c\u0435 \u0432 \u0447\u0430\u0441\u0442 1, \u043f\u043e\u0441\u0442\u0440\u043e\u044f\u0432\u0430\u043c\u0435 \u043c\u043e\u0434\u0435\u043b, \u043e\u043f\u0438\u0441\u0432\u0430\u0449 \u0432\u0437\u0430\u0438\u043c\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f \u043e\u0442 \u0442\u0438\u043f \u0445\u0438\u0449\u043d\u0438\u043a \u2013 \u0436\u0435\u0440\u0442\u0432\u0430 \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0435 \u043f\u043e\u043f\u0443\u043b\u0430\u0446\u0438\u0438. \u0426\u0435\u043b\u0442\u0430 \u043d\u0438 \u0435 \u0434\u0430 \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u043a\u0430\u043a \u0434\u0430\u0434\u0435\u043d \u043c\u043e\u0434\u0435\u043b \u043c\u043e\u0436\u0435 \u0434\u0430 \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 \u043a\u0430\u0442\u043e \u0433\u0440\u0430\u0434\u0438\u0432\u0435\u043d \u0435\u043b\u0435\u043c\u0435\u043d\u0442 \u043d\u0430 \u0434\u0440\u0443\u0433, \u043f\u043e-\u0441\u043b\u043e\u0436\u0435\u043d \u043c\u043e\u0434\u0435\u043b. \u0418\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0430- \u043c\u0435 \u0438 \u043e\u0449\u0435 \u0435\u0434\u043d\u0430 \u043c\u043d\u043e\u0433\u043e \u0432\u0430\u0436\u043d\u0430 \u0442\u0435\u0445\u043d\u0438\u043a\u0430 \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0442\u043e \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u043d\u0435 \u2013 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043c\u043e\u0434\u0435\u043b\u0438, \u0431\u0430\u0437\u0438\u0440\u0430\u043d\u0438 \u043d\u0430 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0438 \u0434\u0430\u043d\u043d\u0438. <\/p>\n<p><em>Keywords<\/em>: mathematical modeling, computer algebra systems, education<\/p>\n<p><strong>MATHEMATICAL MODELS OF REAL PROCESSES AND APPLICATIONS <\/strong><br \/><strong>OF COMPUTER ALGEBRA SYSTEMS TO THEIR STUDY: PART TWO<\/strong><\/p>\n<p><strong>Abstract.<\/strong> This paper is a continuation of the topic we began in issue 5\/2014 of the journal \u201cMathematics and Informatics\u201d. Using the discrete logistic model we talked about in Part 1, we construct a model, describing predator-prey interactions between two populations. Our goal is to show how a model can be used as a building block of another, more complicated model. Also, we illustrate another important technique in mathematical modeling\u2014creating empirical models. <\/p>\n<p><strong>Mr. Tihomir Ivanov, Assist. Prof.<\/strong> <br \/>Faculty of Mathematics and Informatics <br \/>University of Sofia <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=\"art04\">&nbsp;<\/a>A REFINEMENT OF AN INEQUALITY WITH RADICALS <\/strong><\/p>\n<p><strong>\u0160efket Arslanagi\u0107<\/strong> <br \/><em>University of Sarajevo<\/em><\/p>\n<p><strong>Abstract<\/strong>. A new algebraic inequality with radicals is proposed in the paper. Its refinement is considered too. The arithmetic-geometric mean (AM-GM) inequality and the Cauchy-Buniakowsky-Schwarz (CBS) inequality are used in the proofs. <\/p>\n<p><em>Keywords<\/em>: inequality, refinement, radical, AN-GM inequality, CBS inequality, function, minimum.<\/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>AN INEQUALITY FOR A RIGHT TRIANGLE AND ITS GENERALIZATION <\/strong><\/p>\n<p><strong>\u0160efket Arslanagi\u0107<\/strong> <br \/><em>University of Sarajevo<\/em><\/p>\n<p><strong>Abstract<\/strong>. The paper considers a geometrical inequality for a right triangle. Some generalizations are proposed applying Calculus for the proofs. <\/p>\n<p><em>Keywords<\/em>: right triangle, inequality, generalization, function, derivative.<\/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>\u041a\u041e\u041d\u041a\u0423\u0420\u0415\u041d\u0422\u041d\u041e\u0421\u0422, \u041f\u041e\u0420\u041e\u0414\u0415\u041d\u0410 \u041e\u0422 \u0422\u0410\u041d\u0413\u0415\u041d\u0422\u0418 <\/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 \u0417\u0430\u0434\u0430\u0447\u0430 4 \u043e\u0442 \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430\u0442\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043f\u0440\u0435\u0437 2014 \u0433., \u0437\u0430 \u043a\u043e\u044f\u0442\u043e \u0435 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u043e \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435. <\/p>\n<p><em>\u041a\u0435\u0443words<\/em>: conic, tangent, barycentric coordinates, Feuerbach configuration&nbsp;&nbsp;&nbsp; <\/p>\n<p><strong>A CONCURRENCE, GENERATED BY TANGENTS <\/strong><\/p>\n<p><strong>Abstract.<\/strong> The paper considers Problem 4 from the paper of the International Mathematical Olympiad in 2014 and proposes a generalization of it. <\/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><strong><a name=\"art07\">&nbsp;<\/a>\u041f\u0415\u0414\u0410\u041b\u041d\u0410 \u041a\u0420\u0418\u0412\u0410 \u041d\u0410 \u0422\u041e\u0427\u041a\u0410 \u0421\u041f\u0420\u042f\u041c\u041e \u0424\u041e\u0419\u0415\u0420\u0411\u0410\u0425\u041e\u0412\u0410 \u041a\u041e\u041d\u0424\u0418\u0413\u0423\u0420\u0410\u0426\u0418\u042f <\/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 \u0435 \u043e\u043f\u0438\u0441\u0430\u043d\u043e \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u043f\u0435\u0434\u0430\u043b\u043d\u0430 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 \u043e\u0442 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f\u0442\u0430 \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430. <\/p>\n<p><em>Keywords<\/em>: triangle, conic, pedal curve, Feuerbach configuration, GSP.<\/p>\n<p><strong>A PEDAL CURVE OF A POINT WITH RESPECT TO A FEUERBACH CONFIGURATION <\/strong><\/p>\n<p><strong>Abstract.<\/strong> A generalization of the pedal circle notion is described in the paper concerning the triangle geometry.<\/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><strong><a name=\"art08\">&nbsp;<\/a>\u0415\u0412\u0420\u041e\u041f\u0415\u0419\u0421\u041a\u0418 \u0418\u0417\u0421\u041b\u0415\u0414\u041e\u0412\u0410\u0422\u0415\u041b\u0421\u041a\u0418 \u0413\u0420\u0423\u041f\u0418&nbsp; \u0421 \u0418\u041d\u0414\u0423\u0421\u0422\u0420\u0418\u042f\u0422\u0410&nbsp; \u2013&nbsp;&nbsp; \u0422\u0420\u0410\u0414\u0418\u0426\u0418\u0418 \u0418 \u041f\u0420\u0415\u0414\u0418\u0417\u0412\u0418\u041a\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u0410<\/strong><\/p>\n<p><strong>\u0421\u0442\u0435\u0444\u043a\u0430 \u0414\u0438\u043c\u043e\u0432\u0430<\/strong> <br \/><em>Sofia University<\/em><\/p>\n<p><strong>Abstract<\/strong>. \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0446\u0435\u043b\u0438 \u0434\u0430 \u0437\u0430\u043f\u043e\u0437\u043d\u0430\u0435 \u0447\u0438\u0442\u0430\u0442\u0435\u043b\u0438\u0442\u0435 \u0441 \u0435\u0434\u043d\u0430 \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u044f \u0432 \u0415\u0432\u0440\u043e\u043f\u0430, \u0441\u0442\u0430\u0440\u0442\u0438\u0440\u0430\u043b\u0430 \u043f\u0440\u0435\u0437 1968 \u0433. \u0432 \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u044f \u0438\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u043d\u0430 \u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430 \u0432 \u041e\u043a\u0441\u0444\u043e\u0440\u0434 (\u0410\u043d\u0433\u043b\u0438\u044f) \u2013 \u043f\u0440\u043e\u0432\u0435\u0436\u0434\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0435\u0434\u043d\u043e\u0441\u0435\u0434\u043c\u0438\u0447\u043d\u0438 \u0438\u0437\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u0441\u043a\u0438 \u0441\u0435\u043c\u0438\u043d\u0430\u0440\u0438, \u043d\u0430\u0440\u0435\u0447\u0435\u043d\u0438 European Study Groups with Industry (ESGI). \u0429\u0435 \u0441\u043f\u043e\u0434\u0435\u043b\u0438\u043c \u0438 \u043d\u0430\u0448\u0438\u044f \u043e\u043f\u0438\u0442, \u043f\u043e\u043b\u0443\u0447\u0435\u043d \u043e\u0442 \u0443\u0441\u043f\u0435\u0448\u043d\u043e\u0442\u043e \u043f\u0440\u043e\u0432\u0435\u0436\u0434\u0430\u043d\u0435 \u043d\u0430 \u0434\u0432\u0430 \u0442\u0430\u043a\u0438\u0432\u0430 \u0444\u043e\u0440\u0443\u043c\u0430 \u0432 \u0411\u044a\u043b\u0433\u0430\u0440\u0438\u044f \u2013 ESGI\u201995 \u043f\u0440\u0435\u0437 \u0441\u0435\u043f\u0442\u0435\u043c\u0432\u0440\u0438 2013 \u0433. \u0438&nbsp; ESGI\u2019104 \u043f\u0440\u0435\u0437 \u0441\u0435\u043f\u0442\u0435\u043c\u0432\u0440\u0438 2014 \u0433. \u041d\u043e\u043c\u0435\u0440\u0430\u0446\u0438\u044f\u0442\u0430 \u0435 \u0432 \u0440\u0430\u043c\u043a\u0438\u0442\u0435 \u043d\u0430 \u0415\u0432\u0440\u043e\u043f\u0430 \u0438 \u0442\u044f \u043f\u043e\u043a\u0430\u0437\u0432\u0430 \u0432\u0441\u0435 \u043f\u043e-\u0433\u043e\u043b\u044f\u043c\u0430\u0442\u0430 \u043f\u043e\u043f\u0443\u043b\u044f\u0440\u043d\u043e\u0441\u0442 \u043d\u0430 \u0442\u0435\u0437\u0438 \u0441\u044a\u0431\u0438\u0442\u0438\u044f \u2013 \u0437\u0430 \u0442\u043e\u0447\u043d\u043e \u0435\u0434\u043d\u0430 \u0433\u043e\u0434\u0438\u043d\u0430 \u0441\u0430 \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u0438 \u0434\u0435\u0432\u0435\u0442 \u0442\u0430\u043a\u0438\u0432\u0430. <\/p>\n<p><em>Keywords<\/em>: applied mathematics, European Study Groups with Industry, ESGI, industrial mathematics<\/p>\n<p><strong>EUROPEAN STUDY GROUPS WITH INDUSTRY \u2013&nbsp; TRADITIONS AND CHALLENGES<\/strong><\/p>\n<p><strong>Abstract.<\/strong> This article aims to acquaint the readers with a European tradition, started in 1968 in Oxford, England &#8211; the holding of one-week research seminars, called European Study Groups with Industry (ESGI). We will also shear our experience, derived from the successful implementation of two such forums in Bulgaria &#8211; ESGI\u201995 in September 2013 and ESGI\u2019104 &#8211; in September 2014. The numbering is within Europe and it shows the increasing popularity of these scientific events &#8211; for exactly one year nine such were conducted. <\/p>\n<p><strong>Prof. Stefka Dimova, DSc.<\/strong> <br \/>Numerical Methods and Algorithms Department <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>&nbsp;<\/p>","protected":false},"excerpt":{"rendered":"<p>&nbsp;CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 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 \u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430: \u0431\u0435\u043b\u0435\u0436\u043a\u0430 \u0437\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 \u043d\u0430 \u0425\u0430\u0438\u043c\u043e\u0432 [Computer-Generated Mathematics: a Note on the Haimov Triangle] \/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0414\u0435\u043a\u043e \u0414\u0435\u043a\u043e\u0432 \/ Sava Grozdev, Deko Dekov &#8211; \u0441\u0442\u0440. 559 &nbsp; &nbsp;[\/emember_protected] 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 A Refinement of an Inequality with Radicals \/ \u0160efket Arslangi\u0107 &#8211; [&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 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2014 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"&nbsp;CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 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 \u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430: \u0431\u0435\u043b\u0435\u0436\u043a\u0430 \u0437\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 \u043d\u0430 \u0425\u0430\u0438\u043c\u043e\u0432 [Computer-Generated Mathematics: a Note on the Haimov Triangle] \/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0414\u0435\u043a\u043e \u0414\u0435\u043a\u043e\u0432 \/ Sava Grozdev, Deko Dekov &#8211; \u0441\u0442\u0440. 559 &nbsp; &nbsp;[\/emember_protected] EDUCATIONAL 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\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 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 \u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0430\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430: \u0431\u0435\u043b\u0435\u0436\u043a\u0430 \u0437\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 \u043d\u0430 \u0425\u0430\u0438\u043c\u043e\u0432 [Computer-Generated Mathematics: a Note on the Haimov Triangle] \/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0414\u0435\u043a\u043e \u0414\u0435\u043a\u043e\u0432 \/ Sava Grozdev, Deko Dekov &#8211; \u0441\u0442\u0440. 559 &nbsp; &nbsp;[\/emember_protected] EDUCATIONAL RESEARCH \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 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