{"id":41274,"date":"2016-12-02T11:58:00","date_gmt":"2016-12-02T08:58:00","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016\/2016-5\/"},"modified":"2019-06-13T20:18:04","modified_gmt":"2019-06-13T17:18:04","slug":"2016-5","status":"publish","type":"post","link":"https:\/\/pedagogy.azbuki.bg\/en\/matematics\/matharticles2016\/2016-5\/","title":{"rendered":"Annual contents of Mathematics and Informatics, 2016"},"content":{"rendered":"<p style=\"text-align: center;\"><strong>\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u0418 \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0422\u0418\u041a\u0410<\/strong><br \/><strong>MATHEMATICS AND INFORMATICS<\/strong><br \/><strong>BULGARIAN EDUCATIONAL JOURNAL<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>ANNUAL CONTENTS<\/strong><br \/><strong>\u0413\u041e\u0414\u0418\u0428\u041d\u041e \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><\/p>\n<p><strong>PAGES \/ \u0421\u0422\u0420\u0410\u041d\u0418\u0426\u0418<\/strong><br \/>Number 1 \/ \u041a\u043d\u0438\u0436\u043a\u0430 1: 1 &ndash; 104<br \/>Number 2 \/ \u041a\u043d\u0438\u0436\u043a\u0430 2: 105 &ndash; 224<br \/>Number 3 \/ \u041a\u043d\u0438\u0436\u043a\u0430 3: 225 &ndash; 344<br \/>Number 4 \/ \u041a\u043d\u0438\u0436\u043a\u0430 4: 345 &ndash; 456<br \/>Number 5 \/ \u041a\u043d\u0438\u0436\u043a\u0430 5: 457 &ndash; 560<br \/>Number 6 \/ \u041a\u043d\u0438\u0436\u043a\u0430 6: 561 &ndash; 688<\/p>\n<p> <strong>CONTEST PROBLEMS \/ \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><br \/>95 &ndash; 96 \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]<br \/>97 &ndash; 98 \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, 2015 [Solutions of the Contest Problems from issue 2, 2015]<br \/>215 &ndash; 215 \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]<br \/>216 &ndash; 217 \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 3, 2015 [Solutions of the Contest Problems from issue 3, 2015]<br \/>317 &ndash; 317 \u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f [Contest Problems of Issue]<br \/>318 &ndash; 322 \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 4, 2015 [Solutions of the Contest Problems from issue 4, 2015]<br \/>446 &ndash; 446 \u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f [Contest Problems of this Issue]<br \/>447 &ndash; 450 \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 5, 2015 [Solutions of the Contest Problems from Issue 5, 2015]<br \/>548 &ndash; 548 \u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f [Contest Problems of this Issue]<br \/>549 &ndash; 553 \u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u043a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u0431\u0440\u043e\u0439 6, 2015 [Solutions of the Contest Problems from Issue 6, 2015]<br \/>673 &ndash; 674 \u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f [Contest Problems of this Issue]<br \/>675 &ndash; 677 \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 1, 2016 [Solutions of the Contest Problems from Issue 1, 2016]<\/p>\n<p><strong> EDUCATIONAL MATTERS \/&nbsp;<\/strong><strong>EDUCATIONAL ISSUES<\/strong> <br \/>11 &ndash; 28 \u0410\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u0435\u043d \u0438\u043b\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u0435\u043d \u043c\u0435\u0442\u043e\u0434 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0430\u0442\u0430 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [Arithmetical or Algebraic Method in Solving Primary School Mathematical Problems] \/ \u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, \u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430, \u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430 \/ Zdravko Lalchev, Margarita Varbanova, Irina Voutova<br \/>29 &ndash; 42 \u0420\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0434\u0438\u0434\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0435\u0439 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u0438 \u043a\u043e\u043c\u043c\u0443\u043d\u0438\u043a\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0439 \u0432 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0438 \u0442\u0432\u043e\u0440\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u043f\u043e\u0441\u043e\u0431\u043d\u043e\u0441\u0442\u0435\u0439 \u0438 \u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u0438\u0445 \u043d\u0430\u0432\u044b\u043a\u043e\u0432 [Realization of the Didactic Possibilities of the Information and Communication Technologies in the Formation of Creative Skills and The Development of Investigating Habits] \/ \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u0420\u0443\u0441\u0430\u043a\u043e\u0432 \/ Alexander Rusakov<br \/>111 &ndash; 120 \u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \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 \u0432 \u0420\u043e\u0441\u0438\u0438 XVIII \u0432\u0435\u043a\u0430 [Development of the Mathematical Education in Russia in the XVIII Century] \/ \u0422\u0430\u0442\u044c\u044f\u043d\u0430 \u0411\u0443\u0442\u043e\u0440\u0438\u043d\u0430 \/ \u0422atyana Butorina<\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL RESEARCH \/&nbsp;\u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418<\/strong><br \/>43 &ndash; 51 Stationary Numbers \/ Smaiyl Makyshov <br \/>52 &ndash; 72 \u041e\u0431\u0449 \u043f\u043e\u0434\u0445\u043e\u0434 \u0437\u0430 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043c\u0435\u0436\u0434\u0443 \u0440\u0430\u0434\u0438\u0443\u0441\u0438 \u043d\u0430 \u0434\u043e\u043f\u0438\u0440\u0430\u0449\u0438 \u0441\u0435 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438 [A General Approach to Establish Relations Among The Radii of Tangent Circles] \/ \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<br \/>73 &ndash; 82 \u0418\u0437\u0432\u044a\u043d\u043a\u043b\u0430\u0441\u043d\u0438\u0442\u0435 \u0434\u0435\u0439\u043d\u043e\u0441\u0442\u0438 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 &ndash; \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0430\u0442\u0430 \u0444\u043e\u0440\u043c\u0430 \u0437\u0430 \u043c\u043e\u0442\u0438\u0432\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 [Extracurricular Activities in Mathematics &ndash; a Different Form for Student Motivation] \/ \u0417\u0430\u0440\u0430 \u0414\u0430\u043d\u0430\u0438\u043b\u043e\u0432\u0430-\u0421\u0442\u043e\u0439\u043d\u043e\u0432\u0430, \u0418\u0432\u0430\u0439\u043b\u043e \u0421\u0442\u0430\u0440\u0438\u0431\u0440\u0430\u0442\u043e\u0432 \/ Zara Danailova-Stoynova, Ivaylo Staribratov<br \/>121 &ndash; 142 \u041f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0438 \u0441\u044a\u0441 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u0442\u0438\u043f Heron [Programming Experiments with Problems of Heron Type] \/ \u041f\u0430\u0432\u0435\u043b \u0410\u0437\u044a\u043b\u043e\u0432 \/ Pavel Azalov<br \/>143 &ndash; 169 \u041e\u0439\u043b\u0435\u0440-\u0412\u0435\u043d \u0434\u0438\u0430\u0433\u0440\u0430\u043c\u0438 \u0438\u043b\u0438 MZ-\u043a\u0430\u0440\u0442\u0438 \u0432 \u043d\u0430\u0447\u0430\u043b\u043d\u0430\u0442\u0430 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [Euler-Venn Diagrams or MZ-Cards in Primary School Mathematics] \/ \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, \u0418\u0432\u0430\u043d \u0414\u0443\u0448\u043a\u043e\u0432 \/ Zdravko Lalchev, Margarita Varbanova, Irina Voutova, Ivan Doushkov<br \/>231 &ndash; 242 \u0425\u0430\u0440\u0430\u043a\u0442\u0435\u0440 \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0432 \u0443\u0441\u043b\u043e\u0432\u0438\u044f\u0445 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u043e\u0433\u043e \u043e\u0431\u0449\u0435\u0441\u0442\u0432\u0430 [Character of the Contemporary Education in Conditions of Information Society Construction] \/ \u042f\u0440\u043e\u0441\u043b\u0430\u0432 \u0412\u0430\u0433\u0440\u0430\u043c\u0435\u043d\u043a\u043e, \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u0420\u0443\u0441\u0430\u043a\u043e\u0432 \/ Jaroslav Vagramenko, Sava Grozdev, Alexander Rusakov<br \/>243 &ndash; 254 \u0410\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u043e\u0442 XI \u0438 XII \u043a\u043b\u0430\u0441 \u043d\u0430 \u043e\u0431\u043b\u0430\u0441\u0442\u043d\u0438\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0442\u0443\u0440\u043d\u0438\u0440 \u041a\u044a\u0440\u0434\u0436\u0430\u043b\u0438&rsquo; 2015 [Analysis of the Problems and Performance of the Students from 11th and 12th Grades in the Regional Mathematics Tournament Kardzhali&rsquo; 2015] \/ \u0420\u043e\u0441\u0435\u043d \u041d\u0438\u043a\u043e\u043b\u0430\u0435\u0432, \u0419\u043e\u0440\u0434\u0430\u043d \u041f\u0435\u0442\u043a\u043e\u0432 \/ Rosen Nikolaev, Jordan Petkov<br \/>351 &ndash; 367 \u041e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u0414\u0440\u043e\u0437-\u0424\u0430\u0440\u043d\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043e \u043e\u0442 \u043e\u043f\u0438\u0441\u0430\u043d\u043e \u043a\u043e\u043d\u0438\u0447\u043d\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435 [Generalization of Droz-Farny Theorem Defined by a Circum-conic] \/ \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<br \/>368 &ndash; 380 \u0410\u043a\u0442\u0438\u0432\u043d\u043e, \u0443\u0447\u0430\u0441\u0442\u0432\u0430\u0449\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0435 &ndash; \u0442\u0438\u043f \u0438\u043d\u0442\u0435\u0440\u0432\u044e [In-depth Interview] \/ \u0425\u0440\u0438\u0441\u0442\u043e \u0425\u0440\u0438\u0441\u0442\u043e\u0432, \u0425\u0440\u0438\u0441\u0442\u043e \u041a\u0440\u0443\u0448\u043a\u043e\u0432 \/ Hristo Hristov, Hristo Krushkov<br \/>463 &ndash; 479 \u0411\u0430\u0437\u0438\u0442\u0435 \u0434\u0430\u043d\u043d\u0438 \u043a\u0430\u0442\u043e \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e \u0437\u0430 \u043f\u043e-\u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 [Databases as Means for More Qualitative Training in Information Technologies] \/ \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u0414\u0437\u0438\u0432\u0435\u0432 \/ Vesselin Dzivev<br \/>480 &ndash; 492 \u0415xcel \u0432 \u043f\u043e\u043c\u043e\u0449 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f [Using \u0415xcel for Solving Some Exponential Equations] \/ \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430, \u041f\u043b\u0430\u043c\u0435\u043d \u041f\u0435\u043d\u0435\u0432 \/ Diana Stefanova, Plamen Penev<br \/>493 &ndash; 496 An Improvement of the Gerretsen&rsquo;s Inequality for Non-obtuse Triangles \/ &Scaron;efket Arslanagi\u0107<br \/>567 &ndash; 571 \u041f\u0435\u0440\u0432\u044b\u0439 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u044b\u0439 \u0441\u0435\u0442\u0435\u0432\u043e\u0439 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u0441\u043a\u0438\u0439 \u043f\u0440\u043e\u0435\u043a\u0442 \u0443\u0447\u0430\u0449\u0438\u0445\u0441\u044f \u0432 \u0440\u0430\u043c\u043a\u0430\u0445 Mite [First International Net Research Project of Secondary Students in the Frames of Mite] \/ \u041c\u0430\u0440\u0438\u044f \u0428\u0430\u0431\u0430\u043d\u043e\u0432\u0430, \u041c\u0430\u0440\u0438\u043d\u0430 \u0411\u0435\u043b\u043e\u0440\u0443\u043a\u043e\u0432\u0430, \u0420\u043e\u0437\u0430 \u0410\u0442\u0430\u043c\u0443\u0440\u0430\u0442\u043e\u0432\u0430, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Maria Shabanova, Marina Belorukova, Roza Atamuratova, Veselin Nenkov<br \/>572 &ndash; 588 \u041d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0442\u0440\u0430\u0435\u043a\u0442\u043e\u0440\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u044b \u0440\u0430\u0432\u043d\u043e\u0431\u0435\u0434\u0440\u0435\u043d\u043d\u044b\u043c\u0438 \u0422\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430\u043c\u0438 [Some Trajectories Determined by Isosceles Triangles] \/ \u041a\u0441\u0435\u043d\u0438\u044f \u0413\u043e\u0440\u0441\u043a\u0430\u044f, \u0414\u0430\u0440\u044c\u044f \u041a\u043e\u043f\u0442\u0435\u0432\u0430, \u0414\u0430\u043d\u0438\u0438\u043b \u041c\u0438\u043a\u0443\u0440\u043e\u0432, \u0415\u0440\u043a\u0435\u043d \u041c\u0443\u0434\u0435\u0431\u0430\u0435\u0432, \u041a\u0430\u0437\u0431\u0435\u043a \u041c\u0443\u0445\u0430\u043c\u0431\u0435\u0442\u043e\u0432, \u0410\u0434\u0438\u043b\u0431\u0435\u043a \u0422\u0435\u043c\u0438\u0440\u0445\u0430\u043d\u043e\u0432, \u041b\u0438\u043b\u0438 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430, \u0418\u0440\u0438\u043d\u0430 \u0425\u0440\u0438\u0441\u0442\u043e\u0432\u0430, \u0420\u0430\u0434\u0438\u043d\u0430 \u0418\u0432\u0430\u043d\u043e\u0432\u0430 \/ Gorskaya Kseniya, Kopteva Daria, Mikurov Danii, Yerkin Amirzhanovich Mudebaev, Kazbek Batyrbekovich Mukhambetov, Adilbek Timurovich Temirkhanov, Lilly Stefanova, Irina Hristova, Radina Ivanova<br \/>589 &ndash; 598 \u0414\u043e\u043c\u0430\u0448\u043d\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 &ndash; \u043d\u0435\u0434\u0435\u043b\u0438\u043c\u0430 \u0447\u0430\u0441\u0442 \u043e\u0442 \u0443\u0447\u0435\u0431\u043d\u0438\u044f \u043f\u0440\u043e\u0446\u0435\u0441 [The Homework &ndash; an Integral Part of the Educational Process] \/ \u0415\u043b\u0435\u043d\u0430 \u0420\u0430\u0434\u043e\u0432\u0430\u043d\u043e\u0432\u0430 \/ Elena Radovanova<br \/>599 &ndash; 613 \u041d\u044f\u043a\u043e\u0438 \u0433\u0440\u0443\u043f\u0438 \u043b\u043e\u0433\u0430\u0440\u0438\u0442\u043c\u0438\u0447\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u0415xcel [Groups of Logarithmic Equations by the Help of Excel] \/ \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430, \u041f\u043b\u0430\u043c\u0435\u043d \u041f\u0435\u043d\u0435\u0432 \/ Diana Stefanova, Plamen Penev<\/p>\n<p>&nbsp;<\/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><br \/>170 &ndash; 182 \u041e\u0449\u0435 \u0435\u0434\u043d\u0430 \u0438\u0434\u0435\u044f \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f [One More Idea to Solve Trigonometric Equations] \/ \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430, \u041f\u043b\u0430\u043c\u0435\u043d \u041f\u0435\u043d\u0435\u0432 \/ Diyana Stefanova, Plamen Penev<br \/>255 &ndash; 26 \u041c\u0435\u0442\u043e\u0434\u0438 \u0437\u0430 \u0430\u043a\u0442\u0438\u0432\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u043a\u0430\u043d\u0434\u0438\u0434\u0430\u0442-\u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438 \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 [Methods for Active Learning of Prospective Students in Informatics] \/ \u0425\u0440\u0438\u0441\u0442\u043e \u041a\u0440\u0443\u0448\u043a\u043e\u0432 \/ Hristo Krushkov<br \/>269 &ndash; 281 \u0427\u0435\u0432\u0438\u0430\u043d\u0430 \u0438 \u0441\u0438\u043c\u0435\u0434\u0438\u0430\u043d\u0430 \u0432 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a. \u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u043d\u0430 \u0421\u0442\u044e\u0430\u0440\u0442 [Cevian and Symmedian in the Triangle Stewart&rsquo; s Theorem] \/ \u0420\u0443\u043c\u044f\u043d\u0430 \u041d\u0435\u0441\u0442\u043e\u0440\u043e\u0432\u0430 \/ Rumyana Nestorova<br \/>282 &ndash; 293 \u041e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u0427\u0435\u0437\u0430\u0440 \u041a\u043e\u0448\u043d\u0438\u0446\u0430 [A Generalization of a Cesar Koshnica Theorem] \/ \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<br \/>294 &ndash; 308 \u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430\u0442\u0430 \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u043a\u0430: \u0430\u0442\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u043e \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e \u0437\u0430 \u0430\u043a\u0442\u0438\u0432\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 [Computational Linguistics: Attractive Means for Active Learning] \/ \u0425\u0440\u0438\u0441\u0442\u043e \u041a\u0440\u0443\u0448\u043a\u043e\u0432, Hristo Krushkov<br \/>309 &ndash; 316 \u0415\u0434\u043d\u0430 \u043f\u0430\u0440\u0430\u0434\u0438\u0433\u043c\u0430 \u0437\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e [Paradigm for the Education] \/ \u0425\u0430\u0440\u0438 \u0410\u043b\u0435\u043a\u0441\u0438\u0435\u0432 \/ Hari Aleksiev<br \/>381 &ndash; 390 \u0425\u0438\u043f\u043e\u0442\u0435\u0437\u0430\u0442\u0430 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [The hypothesis in teaching mathematics] \/ \u0420\u0443\u043c\u044f\u043d\u0430 \u041c\u0430\u0432\u0440\u043e\u0432\u0430, \u041f\u0435\u043d\u043a\u0430 \u0420\u0430\u043d\u0433\u0435\u043b\u043e\u0432\u0430, \u0415\u043b\u0435\u043d\u0430 \u0422\u043e\u0434\u043e\u0440\u043e\u0432\u0430 \/ Rumyana Mavrova, Penka Rangelova, Elena Todorova<br \/>391 &ndash; 401 Comparative Analysis of the Students&rsquo; Scores in Solving Constructive Tasks when Geometry is Studied in a Standard Way and with the Use of Complex Numbers \/ Katerina Anevska, Risto Malceski, Metodi Glavche<br \/>402 &ndash; 415 \u041f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u0442 \u0442\u0438\u043f PISA, \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u0441\u043e\u0444\u0442\u0443\u0435\u0440 \u0437\u0430 \u043e\u0431\u0449\u043e \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 [A Practical Problem of PISA Type Studied by Software for General Application] \/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0414\u0435\u0441\u0438\u0441\u043b\u0430\u0432\u0430 \u0413\u0435\u043e\u0440\u0433\u0438\u0435\u0432\u0430 \/ Sava Grozdev, Desislava Georgieva<br \/>416 &ndash; 431 \u041e\u0442 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u043d\u043e \u043a\u044a\u043c \u043e\u0431\u0435\u043a\u0442\u043e\u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 [From Structured to \u041ebject-oriented Programming] \/ \u0425\u0440\u0438\u0441\u0442\u043e \u041a\u0440\u0443\u0448\u043a\u043e\u0432 \/ Hristo Krushkov<br \/>432 &ndash; 445 \u041a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438\u0442\u0435 \u0438\u0433\u0440\u0438 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 &ndash; \u043f\u0440\u0435\u0434\u0438\u0437\u0432\u0438\u043a\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430 \u0438 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 [Computer Games in Mathematics Education &ndash; Challenges and Opportunities] \/ \u041c\u0430\u044f \u0421\u0442\u043e\u044f\u043d\u043e\u0432\u0430, \u0414\u0430\u043d\u0438\u0435\u043b\u0430 \u0414\u0443\u0440\u0435\u0432\u0430-\u0422\u0443\u043f\u0430\u0440\u043e\u0432\u0430, \u041a\u043e\u0441\u0442\u0430\u0434\u0438\u043d \u0421\u0430\u043c\u0430\u0440\u0434\u0436\u0438\u0435\u0432 \/ Maya Stoyanova, Daniela Dureva-Tuparova, Kostadin Samardzhiev<br \/>497 &ndash; 504 Three Inequalities for the Altitudes of a Triangle \/ &Scaron;efket Arslanagi\u0107<br \/>505 &ndash; 515 Computer Discovered Mathematics: Orthology Centers of the Euler Triangles \/ Sava Grozdev, Deko Dekov<br \/>516 &ndash; 525 Forecasting of Time-Series for Financial Markets \/ Reinhard Magenreuter<br \/>526 &ndash; 538 Neural Networks \/ Reinhard Magenreuter<br \/>539 &ndash; 547 \u0410\u043a\u0430\u0434\u0435\u043c\u0438\u0447\u043d\u0430\u0442\u0430 \u043b\u0435\u043a\u0446\u0438\u044f &ndash; \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u043e\u043d\u043d\u0430 \u0444\u043e\u0440\u043c\u0430 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u0432\u044a\u0432 \u0432\u0443\u0437 \u0441 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0437\u0430 \u0438\u043d\u043e\u0432\u0430\u0446\u0438\u043e\u043d\u043d\u043e \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 \u043f\u043e\u0437\u043d\u0430\u0432\u0430\u0442\u0435\u043b\u043d\u0438\u044f \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b [The Academic Lecture &ndash; a Traditional Form of Instruction in Higher Education with Possibilities for Innovative Development of Learning Potential] \/ \u0415\u043b\u0435\u043d\u0430 \u0420\u0430\u0434\u043e\u0432\u0430\u043d\u043e\u0432\u0430 \/ Elena Radovanova<br \/>614 &ndash; 625 \u041f\u0441\u0435\u0432\u0434\u043e\u0446\u0435\u043d\u0442\u044a\u0440 \u0438 \u043e\u0440\u0442\u043e\u0446\u0435\u043d\u0442\u044a\u0440 &ndash; \u0437\u0430\u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0435\u043b\u043d\u0438 \u0442\u043e\u0447\u043a\u0438 \u0432 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 [Pseudocenter and Orthocenter &ndash; Notable Points in the Quadrilateral] \/ \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432, \u0421\u0442\u0430\u043d\u0438\u0441\u043b\u0430\u0432 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432, \u0425\u0430\u0438\u043c \u0425\u0430\u0438\u043c\u043e\u0432 \/ Veselin Nenkov, Stanislav Stefanov, Haim Haimov<br \/>626 &ndash; 656 \u041d\u044f\u043a\u043e\u0438 \u043d\u043e\u0432\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u043c\u0435\u0436\u0434\u0443 \u0441\u0440\u0435\u0434\u043d\u0438\u0442\u0435 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u0447\u043d\u043e, \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e, \u0445\u0430\u0440\u043c\u043e\u043d\u0438\u0447\u043d\u043e \u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e [Some New Inequalities Among the Arithmetic, Geometric, Harmonic and Quadratic Means] \/ \u0422\u043e\u0434\u043e\u0440 \u041c\u0438\u0442\u0435\u0432 \/ Todor Mitev<br \/>657 &ndash; 664 Fuzzy Logic \/ Reinhard Magenreuter<br \/>665 &ndash; 672 Genetic Algorithm \/ Reinhard Magenreuter<\/p>\n<p>&nbsp;<\/p>\n<p><strong>OLYMPIADS. COMPETITIONS \/&nbsp;\u041e\u041b\u0418\u041c\u041f\u0418\u0410\u0414\u0418. \u0421\u042a\u0421\u0422\u0415\u0417\u0410\u041d\u0418\u042f<\/strong><br \/>83 &ndash; 88 \u0422\u0440\u0438\u043d\u0430\u0434\u0435\u0441\u0435\u0442\u0430 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043b\u0438\u043d\u0433\u0432\u0438\u0441\u0442\u0438\u043a\u0430 [Thirteenth International Linguistics Olympiad] \/ \u0418\u0432\u0430\u043d \u0414\u0435\u0440\u0436\u0430\u043d\u0441\u043a\u0438 \/ Ivan Derzhanski<br \/>89 &ndash; 94 \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430 \u0416\u0430\u0443\u0442\u0438\u043a\u043e\u0432\u0441\u043a\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434a [International Zhautikov Olympiad] \/ \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<\/p>\n<p>&nbsp;<\/p>\n<p><strong>RESEARCH, SURVEYS, RESULTS \/ \u041f\u0420\u041e\u0423\u0427\u0412\u0410\u041d\u0418\u042f, \u0420\u0415\u0417\u0423\u041b\u0422\u0410\u0422\u0418<\/strong><br \/>183 &ndash; 192 \u041e\u0431\u0432\u044a\u0440\u0437\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f [Connecting the Education in Algebra and Geometry] \/ \u0420\u0443\u043c\u044f\u043d\u0430 \u041c\u0430\u0432\u0440\u043e\u0432\u0430, \u041f\u0435\u043d\u043a\u0430 \u0420\u0430\u043d\u0433\u0435\u043b\u043e\u0432\u0430 \/ Rumiyana Mavrova, Penka Rangelova<br \/>193 &ndash; 203 Comparative Analysis Regarding the Use of Complex Numbers in Secondary School \/ Katerina Anevska, Sava Grozdev, Risto Mal\u010deski<br \/>204 &ndash; 214 \u041c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0430 \u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0447\u043d\u0430 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u043d\u0430 \u0434\u0438\u0434\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e \u043f\u0440\u043e\u0435\u043a\u0442\u0438\u0440\u0430\u043d\u0435 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [Methodical and Technological Realization of Didactical Design in Mathematics Teaching] \/ \u041d\u0430\u0442\u0430\u043b\u0438\u044f \u041f\u0430\u0432\u043b\u043e\u0432\u0430 \/ Nataliya Pavlova<\/p>","protected":false},"excerpt":{"rendered":"<p>\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u0418 \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0422\u0418\u041a\u0410MATHEMATICS AND INFORMATICSBULGARIAN EDUCATIONAL JOURNAL ANNUAL CONTENTS\u0413\u041e\u0414\u0418\u0428\u041d\u041e \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 PAGES \/ \u0421\u0422\u0420\u0410\u041d\u0418\u0426\u0418Number 1 \/ \u041a\u043d\u0438\u0436\u043a\u0430 1: 1 &ndash; 104Number 2 \/ \u041a\u043d\u0438\u0436\u043a\u0430 2: 105 &ndash; 224Number 3 \/ \u041a\u043d\u0438\u0436\u043a\u0430 3: 225 &ndash; 344Number 4 \/ \u041a\u043d\u0438\u0436\u043a\u0430 4: 345 &ndash; 456Number 5 \/ \u041a\u043d\u0438\u0436\u043a\u0430 5: 457 &ndash; 560Number 6 \/ \u041a\u043d\u0438\u0436\u043a\u0430 6: 561 &ndash; 688 [&hellip;]<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[]},"categories":[3290],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - 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