{"id":40892,"date":"2016-04-07T21:59:00","date_gmt":"2016-04-07T18:59:00","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016\/mathinfocontent022016\/"},"modified":"2019-06-18T21:58:29","modified_gmt":"2019-06-18T18:58:29","slug":"mathinfocontent022016","status":"publish","type":"post","link":"https:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles2016\/mathinfocontent022016\/","title":{"rendered":"Mathematics and Informatics, Number 2\/2016, Volume 59"},"content":{"rendered":"<p><strong><a name=\"top\"><br \/> <\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL MATTERS \/&nbsp;<br \/><\/strong><strong>EDUCATIONAL ISSUES<\/strong><\/p>\n<p><a href=\"#art01\"> \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 <br \/>[Development of the Mathematical Education in Russia in the XVIII Century] <\/a>\/<br \/> \u0422\u0430\u0442\u044c\u044f\u043d\u0430 \u0411\u0443\u0442\u043e\u0440\u0438\u043d\u0430 \/ \u0422atyana Butorina &ndash; \u0441\u0442\u0440. 111<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/06\/azbuki.bg_dmdocuments_Matematika_02_2016_Tatyana-Butorina.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL RESEARCH \/<\/strong><br \/><strong> EDUCATIONAL MATTERS<\/strong><\/p>\n<p><a href=\"#art02\"> \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<br \/> [Programming Experiments with Problems of Heron Type] <\/a>\/ <br \/>\u041f\u0430\u0432\u0435\u043b \u0410\u0437\u044a\u043b\u043e\u0432 \/ Pavel Azalov &nbsp;&ndash; \u0441\u0442\u0440. 121<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/06\/azbuki.bg_dmdocuments_Matematika_02_2016_Pavel-Azalov.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art03\"> \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 <br \/>[Euler-Venn Diagrams or MZ-Cards in Primary School Mathematics] <\/a>\/ <br \/>\u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, \u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430, \u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430, \u0418\u0432\u0430\u043d \u0414\u0443\u0448\u043a\u043e\u0432 \/<br \/> Zdravko Lalchev, Margarita Varbanova, Irina Voutova, Ivan Doushkov &ndash; \u0441\u0442\u0440. 143<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/06\/azbuki.bg_dmdocuments_Matematika_02_2016_Zdravko-Lalchev_Margarita-Varbanova_Irina-Voutova_Ivan-Doushkov.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>EDUCATIONAL TECHNOLOGIES \/ <\/strong><br \/><strong>EDUCATIONAL TECHNOLOGIES<\/strong><\/p>\n<p><a href=\"#art04\"> \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 <br \/>[One More Idea to Solve Trigonometric Equations] <\/a>\/ <br \/>\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 &nbsp;&ndash; \u0441\u0442\u0440. 170<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/06\/azbuki.bg_dmdocuments_Matematika_02_2016_Diyana-Stefanova_Plamen-Penev.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>RESEARCH, SURVEYS, RESULTS \/<\/strong><br \/><strong>\u041f\u0420\u041e\u0423\u0427\u0412\u0410\u041d\u0418\u042f, \u0420\u0415\u0417\u0423\u041b\u0422\u0410\u0422\u0418<\/strong><\/p>\n<p><a href=\"#art05\"> \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 <br \/>[Connecting the Education in Algebra and Geometry] <\/a>\/ <br \/>\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 &ndash; \u0441\u0442\u0440. 183<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/06\/azbuki.bg_dmdocuments_Matematika_02_2016_Rumiyana-Mavrova_Penka-Rangelova.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art06\"> Comparative Analysis Regarding the Use of Complex Numbers in Secondary School <\/a>\/<br \/> Katerina Anevska, Sava Grozdev, Risto Mal\u010deski &ndash; \u0441\u0442\u0440. 193<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/06\/azbuki.bg_dmdocuments_Matematika_02_2016_Katerina-Anevska_Sava-Grozdev_Risto-Malceski.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"#art07\"> \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 <br \/>[Methodical and Technological Realization of Didactical Design in Mathematics Teaching] <\/a>\/ <br \/>\u041d\u0430\u0442\u0430\u043b\u0438\u044f \u041f\u0430\u0432\u043b\u043e\u0432\u0430 \/ Nataliya Pavlova &ndash; \u0441\u0442\u0440. 204<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/06\/azbuki.bg_dmdocuments_Matematika_02_2016_Nataliya-Pavlova.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>CONTEST PROBLEMS \/<\/strong><br \/><strong> CONTEST PROBLEMS<\/strong><\/p>\n<p>Contest Problems of this Issue<br \/> [Contest Problems of the Issue] &ndash; \u0441\u0442\u0440. 215<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/06\/azbuki.bg_dmdocuments_Matematika_02_2016_Contest-Problems.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>\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 <br \/>[Solutions of the Contest Problems from issue 6, 2015] &ndash; \u0441\u0442\u0440. 216<\/p>\n<p><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2016\/06\/azbuki.bg_dmdocuments_Matematika_02_2016_Solutions.pdf\" class=\"doclink\"><img decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-38022\" src=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" alt=\"icon\" border=\"0\" width=\"16\" height=\"16\" \/>&nbsp;Open the full text<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>READINTHELATESTISSUESOF &bdquo;AZBUKI&ldquo; 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 &bdquo;\u0410\u0417 \u0411\u0423\u041a\u0418&ldquo; \u0427\u0415\u0422\u0415\u0422\u0415<\/strong> &ndash; \u0441\u0442\u0440. 218<\/p>\n<p>&nbsp;<\/p>\n<p><strong>GUIDEFORAUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u042f \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/strong> &ndash; \u0441\u0442\u0440. 220<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p class=\"zaglavie\"><strong><a name=\"atr01\"><\/a> \u0420\u0410\u0417\u0412\u0418\u0422\u0418\u0415 \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 \u0412 \u0420\u041e\u0421\u0421\u0418\u0418 XVIII \u0412\u0415\u041a\u0410<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p class=\"avtor\">\u0422\u0430\u0442\u044c\u044f\u043d\u0430 \u0411\u0443\u0442\u043e\u0440\u0438\u043d\u0430<\/p>\n<p class=\"avtor-titla\">\u041b\u043e\u043c\u043e\u043d\u043e\u0441\u043e\u0432\u0441\u043a\u0438\u0439 \u0438\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0421\u0410\u0424\u0423<\/p>\n<p class=\"avtor-titla\"><strong>&nbsp;<\/strong><\/p>\n<p class=\"anotacia\"><strong>\u0420\u0435\u044d\u044e\u043c\u0435.<\/strong> \u0412 \u0434\u0430\u043d\u043d\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043d\u044b \u0442\u0440\u0430\u0434\u0438\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 \u0432 \u0420\u043e\u0441\u0441\u0438\u0438 \u0425VIII \u0432\u0435\u043a\u0430. \u041e\u043d\u0438 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u044b \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0438 \u043a\u043b\u0430\u0441\u0441\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u0446\u0430, \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u043c\u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f\u043c\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0441\u0432\u0435\u0442\u0441\u043a\u043e\u0441\u0442\u044c \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f, \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u0438 \u043d\u0430\u0443\u0447\u043d\u043e\u0441\u0442\u044c.<\/p>\n<p class=\"anotacia\"><em>Keywords<\/em>: education, university, tradition, science, fundamental knowledge<\/p>\n<hr \/>\n<p><strong><a name=\"atr02\"><\/a> DEVELOPMENT OF THE MATHEMATICAL EDUCatION IN RUSSIA IN THE XVIIICENTURY<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>\u0410bstract. The present paper considers the traditions of the mathematical education in Russia in the \u0425VIII century. They are based on a classic type of education, whose main characteristics are secularity, fundamentality and scientific content.<\/p>\n<p>&nbsp;<\/p>\n<p>Prof. Tatyana Butorina, DSc<\/p>\n<p>Director<\/p>\n<p>Lomonosov Institute, NAFU<\/p>\n<hr \/>\n<p><strong><a name=\"atr03\"><\/a>\u041f\u0420\u041e\u0413\u0420\u0410\u041c\u041d\u0418 \u0415\u041a\u0421\u041f\u0415\u0420\u0418\u041c\u0415\u041d\u0422\u0418 \u0421\u042a\u0421 \u0417\u0410\u0414\u0410\u0427\u0418 \u041e\u0422 \u0422\u0418\u041f HERON<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Pavel Azalov<\/p>\n<p>\u041f\u0435\u043d\u0441\u0438\u043b\u0432\u0430\u043d\u0441\u043a\u0438 \u0434\u044a\u0440\u0436\u0430\u0432\u0435\u043d \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0417\u0430\u0434\u0430\u0447\u0430\u0442\u0430 \u043d\u0430 Heron \u0435 \u0434\u0440\u0435\u0432\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430 \u0437\u0430\u0434\u0430\u0447\u0430, \u043a\u043e\u044f\u0442\u043e \u0438\u043c\u0430 \u0442\u043e\u0447\u043d\u043e \u0438 \u0435\u043b\u0435\u0433\u0430\u043d\u0442\u043d\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435.<\/p>\n<p>\u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0430\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438, \u043a\u043e\u0438\u0442\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0432\u0430\u0442 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430\u0442\u0430 \u043d\u0430 Heron, \u043d\u043e \u0437\u0430 \u043a\u043e\u0438\u0442\u043e \u043d\u0435 \u0441\u0430 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0438 \u0442\u043e\u0447\u043d\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f. \u0422\u0435\u0437\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0438\u043c\u0430\u0442 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u043e \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0438 \u0437\u0430 \u0442\u044f\u0445 \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0447\u0440\u0435\u0437 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438 \u043d\u0430 C++ \u0438 MATLAB.<\/p>\n<p>&nbsp;<\/p>\n<p>Keywords: Heron type problems, Generalized Heron problems<\/p>\n<p>&nbsp;<\/p>\n<p><strong>PROGRAMMING EXPERIMENTS WITH PROBLEMS OF HERON TYPE<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. The Heron&#8217;s problem is an ancient mathematical problem, which has a precise and elegant solution. The paper discusses generalizations of the Heron problem that have a variety of practical applications. Nowadays, it is still unknown if such problems have precise mathematical solutions. Approximate solutions to similar problems written as programs in C++ and MATLAB are presented in this paper.<\/p>\n<p>&nbsp;<\/p>\n<p>Dr. Pavel Azalov<\/p>\n<p>Assoc. Prof. of Computer Science<\/p>\n<p>Pennsylvania State University<\/p>\n<hr \/>\n<p><strong><a name=\"atr04\"><\/a> \u0419\u041b\u0415\u0420-\u0412\u0415\u041d \u0414\u0418\u0410\u0413\u0420\u0410\u041c\u0418 \u0418\u041b\u0418 MZ-\u041a\u0410\u0420\u0422\u0418 \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>&nbsp;<\/p>\n<p>\u041c\u0430\u0440\u0433\u0430\u0440\u0438\u0442\u0430 \u0412\u044a\u0440\u0431\u0430\u043d\u043e\u0432\u0430<\/p>\n<p>\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 &bdquo;\u0421\u0432. \u0441\u0432. \u041a\u0438\u0440\u0438\u043b \u0438 \u041c\u0435\u0442\u043e\u0434\u0438\u0439&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p>\u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, \u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430, \u0418\u0432\u0430\u043d \u0414\u0443\u0448\u043a\u043e\u0432<\/p>\n<p>\u0421\u043e\u0444\u0438\u0439\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 &bdquo;\u0421\u0432. \u041a\u043b\u0438\u043c\u0435\u043d\u0442 \u041e\u0445\u0440\u0438\u0434\u0441\u043a\u0438&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u041f\u0440\u0435\u0434\u043c\u0435\u0442\u044a\u0442 \u043d\u0430 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u043e\u0441\u0442\u0440\u043e\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043c\u043e\u0434\u0435\u043b\u0438 \u043d\u0430 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u043d\u0438 \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0438, \u043f\u043e\u0440\u043e\u0434\u0435\u043d\u0438 \u043e\u0442 \u0430\u0434\u0438\u0442\u0438\u0432\u043d\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 (\u043e\u0431\u0435\u0434\u0438\u043d\u044f\u0432\u0430\u043d\u0435, \u043f\u0440\u0435\u0441\u0438\u0447\u0430\u043d\u0435 \u0438 \u0434\u043e\u043f\u044a\u043b\u0432\u0430\u043d\u0435) \u0441 \u043a\u0440\u0430\u0439\u043d\u0438 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \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. \u041d\u0430\u043f\u0440\u0430\u0432\u0435\u043d \u0435 \u0441\u0440\u0430\u0432\u043d\u0438\u0442\u0435\u043b\u0435\u043d \u0430\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0434\u0432\u0430 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u043e\u0434\u0445\u043e\u0434\u0430 \u0437\u0430 \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u043d\u0435 \u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u0430\u0434\u0438\u0442\u0438\u0432\u043d\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0441 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u0438 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u0438 \u0447\u0438\u0441\u043b\u0430. \u0421\u0442\u0430\u0432\u0430 \u0434\u0443\u043c\u0430 \u0437\u0430 \u0434\u043e\u0431\u0438\u043b\u0438\u044f \u0432\u0435\u0447\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0441\u0442 \u043c\u0435\u0442\u043e\u0434 \u043d\u0430 &bdquo;\u041e\u0439\u043b\u0435\u0440-\u0412\u0435\u043d \u0434\u0438\u0430\u0433\u0440\u0430\u043c\u0438\u0442\u0435&ldquo; \u0438 \u0437\u0430 \u0438\u043d\u043e\u0432\u0430\u0442\u0438\u0432\u043d\u0438\u044f \u043c\u0435\u0442\u043e\u0434 \u043d\u0430 &bdquo;MZ-\u043a\u0430\u0440\u0442\u0438\u0442\u0435&ldquo;. \u041f\u0440\u043e\u043a\u0430\u0440\u0430\u043d\u0430 \u0435 \u0438\u0434\u0435\u044f\u0442\u0430, \u0447\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u0442\u043e \u043c\u043e\u0436\u0435 \u0434\u0430 \u0431\u044a\u0434\u0435 \u043d\u0430\u043c\u0435\u0440\u0435\u043d\u043e \u043f\u043e-\u043b\u0435\u0441\u043d\u043e, \u0430\u043a\u043e \u043f\u0440\u0438 \u0441\u044a\u0441\u0442\u0430\u0432\u044f\u043d\u0435 \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043c\u043e\u0434\u0435\u043b \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430\u0442\u0430 \u0434\u0432\u0430\u0442\u0430 \u043f\u043e\u0434\u0445\u043e\u0434\u0430 \u0441\u0435 \u0434\u043e\u043f\u044a\u043b\u0432\u0430\u0442.<\/p>\n<p>Keywords: primary school mathematics, MZ-card, Euler-Venn diagram, mathematical model<\/p>\n<p>&nbsp;<\/p>\n<p><strong>EULER-VENN DIAGRAMS OR MZ-CARDS IN PRIMARY SCHOOL MATHEMATICS<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. The subject of the paper is the mathematical model construction of problem situations, caused by additive operations (union, intersection and supplement) with finite sets in primary school mathematics. A comparative analysis of two methodological approaches for modeling and solving problems for additive operations and natural numbers is done. It is about the already known &bdquo;Euler-Venn diagram&ldquo; method and the innovative &bdquo;MZ-card&ldquo; method. An idea is drawn that a solution could be found easier, if the two approaches complement one another in the construction of the mathematical model of the problem.<\/p>\n<p>&nbsp;<\/p>\n<p>Prof. Dr. Zdravko Lalchev<\/p>\n<p>Faculty of Preschool and Primary Education<\/p>\n<p>University of Sofia<\/p>\n<p>&nbsp;<\/p>\n<p>Prof. Dr. Margarita Varbanova<\/p>\n<p>Faculty of Mathematics and Informatics<\/p>\n<p>University of VelikoTarnovo<\/p>\n<p>&nbsp;<\/p>\n<p>Dr. Irina Voutova, Assist. Prof.<\/p>\n<p>Faculty of Mathematics and Informatics<\/p>\n<p>Sofia University<\/p>\n<p>&nbsp;<\/p>\n<p>Dr. Ivan Doushkov, Assist. Prof.<\/p>\n<p>Faculty of Preschool and Primary Education<\/p>\n<p>University of Sofia<\/p>\n<hr \/>\n<p><strong><a name=\"atr05\"><\/a> \u041e\u0429\u0415 \u0415\u0414\u041d\u0410 \u0418\u0414\u0415\u042f \u0417\u0410 \u0420\u0415\u0428\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u0422\u0420\u0418\u0413\u041e\u041d\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0418 \u0423\u0420\u0410\u0412\u041d\u0415\u041d\u0418\u042f<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>\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<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430 \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\u0437\u0430 \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0430 \u043d\u0430 \u0438\u0434\u0435\u0438, \u0445\u0440\u0443\u043c\u0432\u0430\u043d\u0438\u044f \u0438 \u0434\u043e\u0433\u0430\u0434\u043a\u0438\u0432 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u043d\u0438 \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0438, \u043a\u043e\u0438\u0442\u043e \u0432\u044a\u0437\u043d\u0438\u043a\u0432\u0430\u0442 \u043f\u0440\u0438 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435\u0442\u043e \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.<\/p>\n<p>&nbsp;<\/p>\n<p>Keywords: problem solving, trigonometric equation, number, table, macros<\/p>\n<p>&nbsp;<\/p>\n<p><strong>ONE MORE IDEA TO SOLVE TRIGONOMETRIC EQUATIONS<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. The experimental environment Excel is used in the paper to check ideas, occurring and guesses in problem situations, which appear in solving trigonometric equations.<\/p>\n<p>Dr. Diyana Stefanova, Mr. Plamen Penev<\/p>\n<hr \/>\n<p><strong><a name=\"atr06\"><\/a> \u041e\u0411\u0412\u042a\u0420\u0417\u0412\u0410\u041d\u0415 \u041d\u0410 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u0410\u041b\u0413\u0415\u0411\u0420\u0410 \u0418 \u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u042f<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>\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<\/p>\n<p>\u041f\u043b\u043e\u0432\u0434\u0438\u0432\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 &bdquo;\u041f\u0430\u0438\u0441\u0438\u0439 \u0425\u0438\u043b\u0435\u043d\u0434\u0430\u0440\u0441\u043a\u0438&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u043f\u043e\u043a\u0430\u0437\u0432\u0430\u043c\u0435 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u0431\u0435\u0437\u043a\u0440\u0430\u0439\u043d\u043e \u043c\u0430\u043b\u043a\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0430 \u043f\u0440\u043e\u0433\u0440\u0435\u0441\u0438\u044f \u0432 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f\u0442\u0430. \u0417\u0430 \u0446\u0435\u043b\u0442\u0430 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u043c\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438, \u0438\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u0430\u0449\u0438 \u0442\u0430\u0437\u0438 \u0432\u0440\u044a\u0437\u043a\u0430.<\/p>\n<p>Keywords: interdisciplinary relations, infinitely small geometric series<\/p>\n<p>&nbsp;<\/p>\n<p><strong>CONNECTING THE EDUCATION IN ALGEBRA AND GEOMETRY<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. It is shown in the present paper the application of infinitely small geometric progressions in geometry. A system of tasks is proposed for the purpose, that illustrate the corresponding relation.<\/p>\n<p>&nbsp;<\/p>\n<p>Dr. Rumiyana Mavrova, Assoc. Prof.<\/p>\n<p>Faculty of Mathematics and Informatics<\/p>\n<p>Plovdiv University &ldquo;Paisiy Hilendarskiy&ldquo;<\/p>\n<p>&nbsp;<\/p>\n<p>Prof. Penka Rangelova, DSc<br \/> Faculty of Mathematics and Informatics<\/p>\n<p>Plovdiv University &ldquo;Paisiy Hilendarskiy&ldquo;<\/p>\n<hr \/>\n<p><strong><a name=\"atr07\"><\/a> COMPARATIVE ANALYSIS REGARDING THE USE OF COMPLEX NUMBERS IN SECONDARY SCHOOL<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. The study of Euclidean plane geometry is compulsory for high school students. Practice shows that even the most advanced students face difficulties when learning this material, and especially the content related to the metric characteristics of the geometric figures and their use. On the other hand, the high school syllabus also includes complex numbers, characterized by an analytical apparatus, which is adequate for learning Euclidean plane geometry. This paper presents the results of a comparative analysis of the scores of the students related to the metric characteristics of the geometric figures in the Euclidean plane and their use, when studied with the use of complex numbers (Malcheski, Grozdev &amp; Anevska, 2015), and when studied in a standard way (Mitrovi\u0107 &amp; al., 1998).<\/p>\n<p>&nbsp;<\/p>\n<p>Keywords: complex number, triangle, circle, test, hypothesis.<\/p>\n<p>&nbsp;<\/p>\n<p>Dr. Katerina Anevska<\/p>\n<p>Faculty of Informatics<\/p>\n<p>First Private University &ndash; FON<\/p>\n<p>Skopje, Macedonia<\/p>\n<p>&nbsp;<\/p>\n<p>*Prof. Sava Grozdev, DSc<\/p>\n<p>University of Finance, Business and Entrepreneurship<\/p>\n<p>&nbsp;Sofia, Bulgaria<\/p>\n<p>&nbsp;<\/p>\n<p>Prof. Risto Malcheski, DSc<\/p>\n<p>Faculty of Informatics<\/p>\n<p>First Private University &ndash; FON<\/p>\n<p>Skopje, Macedonia<\/p>\n<hr \/>\n<p><strong>8 \u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0410 \u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0427\u041d\u0410 \u0420\u0415\u0410\u041b\u0418\u0417\u0410\u0426\u0418\u042f \u041d\u0410 \u0414\u0418\u0414\u0410\u041a\u0422\u0418\u0427\u0415\u0421\u041a\u041e \u041f\u0420\u041e\u0415\u041a\u0422\u0418\u0420\u0410\u041d\u0415 \u0412 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Nataliya Pavlova<\/p>\n<p>University of Shumen<\/p>\n<p>&nbsp;<\/p>\n<p>\u0420\u0435\u0437\u044e\u043c\u0435. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0430 \u0438\u0434\u0435\u044f \u0437\u0430 \u043f\u0430\u0440\u0430\u043b\u0435\u043b\u043d\u043e \u0444\u043e\u0440\u043c\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0443\u043c\u0435\u043d\u0438\u044f \u0437\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 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0430 \u0438 \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u043e\u043d\u043d\u0430 \u0444\u043e\u0440\u043c\u0430. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d \u0435 \u043a\u043e\u043d\u0446\u0435\u043f\u0442\u0443\u0430\u043b\u0435\u043d \u043c\u043e\u0434\u0435\u043b \u0437\u0430 \u043e\u0441\u044a\u0449\u0435\u0441\u0442\u0432\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0442\u0430\u0437\u0438 \u0438\u0434\u0435\u044f \u0432 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u0443\u0440\u0441 \u0437\u0430 \u0431\u044a\u0434\u0435\u0449\u0438 \u0443\u0447\u0438\u0442\u0435\u043b\u0438. \u041f\u043e\u0441\u043e\u0447\u0435\u043d\u0438 \u0441\u0430 \u043d\u044f\u043a\u043e\u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u043d\u0430 \u043f\u043b\u0430\u0442\u0444\u043e\u0440\u043c\u0438 \u0437\u0430 <br \/> \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0435 \u043d\u0430 \u043f\u043b\u0430\u043d-\u043a\u043e\u043d\u0441\u043f\u0435\u043a\u0442\u0438 \u0438 \u0441\u043e\u0444\u0442\u0443\u0435\u0440 \u0437\u0430 \u0441\u044a\u0437\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u0442\u0434\u0435\u043b\u043d\u0438 \u0434\u0438\u0434\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0438 \u0437\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043a\u043e\u0438\u0442\u043e \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0441\u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u0442 \u043f\u0440\u0438 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435 \u043d\u0430 \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u044f \u043c\u043e\u0434\u0435\u043b.<\/p>\n<p>&nbsp;<\/p>\n<p>Keywords: education, mathematics, digital materials, learning design<\/p>\n<p>&nbsp;<\/p>\n<p><strong>METHODICAL AND TECHNOLOGICAL REALIZATIONOF DIDACTICAL DESIGNIN MATHEMATICS TEACHING<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Abstract. The paper presents the idea of parallel formation of skills for didactic design in electronic and traditional form. A conceptual model is proposed to realize this idea in a methodological course for future teachers. Some concrete examples of platforms are shown to describe teaching scenarios and software to create didactic materials for mathematical teaching, which can be used in applying the described model.<\/p>\n<p>&nbsp;<\/p>\n<p>Dr. Nataliya Pavlova, Assoc. Prof.<\/p>\n<p>Shumen University &bdquo;Konstantin Preslavski&ldquo;<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>","protected":false},"excerpt":{"rendered":"<p>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 &nbsp; EDUCATIONAL MATTERS \/&nbsp;\u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e \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 &ndash; \u0441\u0442\u0440. 111 &nbsp;\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 &nbsp; 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 \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 [&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 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ 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MATTERS \/&nbsp;\u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e \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 &ndash; \u0441\u0442\u0440. 111 &nbsp;\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 &nbsp; 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 \u041f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0438 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