{"id":42509,"date":"2018-03-01T12:24:20","date_gmt":"2018-03-01T09:24:20","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016-3\/1-lxi-2018\/"},"modified":"2019-06-18T21:58:27","modified_gmt":"2019-06-18T18:58:27","slug":"1-lxi-2018","status":"publish","type":"post","link":"https:\/\/newspaper.azbuki.bg\/en\/matematics\/matharticles2016-3\/1-lxi-2018\/","title":{"rendered":"Mathematics and Informatics, Number 1\/2018, Volume 61"},"content":{"rendered":"<p><a name=\"top\"><\/a><strong>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>EDITORIAL \/ \u041a\u042a\u041c \u0427\u0418\u0422\u0410\u0422\u0415\u041b\u042f<\/strong> \u2013 p. 7<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2018\/02\/azbuki.bg_dmdocuments_Matematika_01_2018_Editorial.pdf\"><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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><strong>EDUCATIONAL MATTERS \/ \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 \/><a href=\"#art01\">Computer Discovered Mathematics: Constructions of Malfatti Squares <\/a><br \/><a href=\"#art01\">[\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043e\u0442\u043a\u0440\u0438\u0442\u0430 \u043e\u0442 \u043a\u043e\u043c\u043f\u044e\u0442\u0440\u0438: \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438 \u043d\u0430 \u043a\u0432\u0430\u0434\u0430\u0442\u0438\u0442\u0435 \u043d\u0430 \u041c\u0430\u043b\u0444\u0430\u0442\u0438] <\/a><br \/>\/ Sava Grozdev, Hiroshi Okumura, Deko Dekov \u2013 \u0441\u0442\u0440. 10<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2018\/02\/azbuki.bg_dmdocuments_Matematika_01_2018_Grozdev_Okumura_Dekov.pdf\"><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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a>\u00a0\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art02\">\u0414\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u043d\u0438 \u0442\u043e\u0447\u043a\u043e\u0432\u0438 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438. \u041f\u0440\u0430\u0432\u0438\u043b\u043e \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430. \u0418\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u0438 <\/a><br \/><a href=\"#art02\">[Diagonal Configurations of Points. Triangle Rule. Invariants] <\/a><br \/>\/ \u0417\u0434\u0440\u0430\u0432\u043a\u043e \u041b\u0430\u043b\u0447\u0435\u0432, \u0418\u0440\u0438\u043d\u0430 \u0412\u0443\u0442\u043e\u0432\u0430 \/ Zdravko Lalchev, Irina Voutova \u2013 \u0441\u0442\u0440. 19<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2018\/02\/azbuki.bg_dmdocuments_Matematika_01_2018_Lalchev_Voutova.pdf\"><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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><a href=\"#art03\">\u041e\u0441\u044a\u0449\u0435\u0441\u0442\u0432\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0432\u044a\u0442\u0440\u0435\u0448\u043d\u043e\u043f\u0440\u0435\u0434\u043c\u0435\u0442\u043d\u0438 \u0432\u0440\u044a\u0437\u043a\u0438 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u2013 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043f\u0440\u043e\u0433\u0440\u0435\u0441\u0438\u0438 <\/a><br \/><a href=\"#art03\">[Realization of Interdisciplinary Connections in Mathematics Training \u2013 Trigonometric Functions and Progressions] <\/a><br \/>\/ \u0417\u0430\u0440\u0430 \u0414\u0430\u043d\u0430\u0438\u043b\u043e\u0432\u0430-\u0421\u0442\u043e\u0439\u043d\u043e\u0432\u0430, \u041f\u0435\u0442\u044a\u0440 \u0414\u0430\u043d\u0447\u0435\u0432 \/ Zara Danailova-Stoynova, Peter Danchev \u2013 \u0441\u0442\u0440. 49<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2018\/02\/azbuki.bg_dmdocuments_Matematika_01_2018_Danailova-Stoynova_Danchev.pdf\"><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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p>\u00a0<\/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><br \/><a href=\"#art04\">\u0420\u0430\u0432\u043d\u043e\u043b\u0438\u0446\u0435\u0432\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438 \u043e\u0442 \u0434\u0432\u0435 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0432\u0430\u043d\u0438\u044f \u0432 \u0440\u0430\u0432\u043d\u0438\u043d\u0430\u0442\u0430 \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a <\/a><br \/><a href=\"#art04\">[Triangles With Equal Areas, Generated by Two Transformations in the Triangle Plane] <\/a><br \/>\/ \u0418\u0432\u0430\u043d \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432, \u0414\u0435\u044f\u043d \u0414\u0438\u043c\u0438\u0442\u0440\u043e\u0432, \u0411\u043e\u0440\u0438\u0441\u043b\u0430\u0432 \u0411\u043e\u0440\u0438\u0441\u043e\u0432 \/ Ivan Stefanov, Deyan Dimitrov, Borislav Borisov \u2013 \u0441\u0442\u0440. 60<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2018\/02\/azbuki.bg_dmdocuments_Matematika_01_2018_Stefanov_Dimitrov_Borisov.pdf\"><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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p><a href=\"#art05\">\u0412\u0440\u044a\u0437\u043a\u0438 \u043c\u0435\u0436\u0434\u0443 \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 <\/a><br \/><a href=\"#art05\">[Connections among Notable Points in the Quadrilateral] <\/a><br \/>\/ \u0421\u0442\u0430\u043d\u0438\u0441\u043b\u0430\u0432 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Stanislav Stefanov, Veselin Nenkov \u2013 \u0441\u0442\u0440. 73<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2018\/02\/azbuki.bg_dmdocuments_Matematika_01_2018_Stefanov_Nenkov.pdf\"><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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p><a href=\"#art06\">\u0422\u0440\u043e\u0439\u043a\u0438 \u0446\u0435\u043d\u0442\u0440\u0430\u043b\u043d\u0438 \u043a\u043e\u043d\u0438\u0447\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0437 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430 \u0442\u043e\u0447\u043a\u0430 \u0432\u044a\u0440\u0445\u0443 \u043a\u043e\u043d\u0438\u0447\u043d\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435 <\/a><br \/><a href=\"#art06\">[Central Conic Triplets Through a Fixed Point on a Fixed Conic] <\/a><br \/>\/ \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 \u2013 \u0441\u0442\u0440. 83<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2018\/02\/azbuki.bg_dmdocuments_Matematika_01_2018_Grozdev_Nenkov.pdf\"><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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><strong>CONTEST PROBLEMS \/ \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><br \/>Contest Problems of this Issue <br \/>[Contest Problems of this Issue] \u2013 \u0441\u0442\u0440. 94<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2018\/02\/azbuki.bg_dmdocuments_Matematika_01_2018_ContestProblems.pdf\"><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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open 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 2, 2017 <br \/>[Solutions of the Contest Problems from Issue 2, 2017] \u2013 \u0441\u0442\u0440. 95<br \/><a href=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2018\/02\/azbuki.bg_dmdocuments_Matematika_01_2018_ContestProblems_reshenia.pdf\"><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\" border=\"0\" alt=\"icon\" width=\"16\" height=\"16\" \/>\u00a0Open the full text<\/a><\/p>\n<p>\u00a0<\/p>\n<p><strong>READ IN THE LATEST ISSUES OF \u201eAZBUKI\u201c JOURNALS <br \/>\/ \u0412 \u041d\u041e\u0412\u0418\u0422\u0415 \u0411\u0420\u041e\u0415\u0412\u0415 \u041d\u0410 \u0421\u041f\u0418\u0421\u0410\u041d\u0418\u042f\u0422\u0410 \u041d\u0410 \u0418\u0417\u0414\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u041e \u201e\u0410\u0417 \u0411\u0423\u041a\u0418\u201c \u0427\u0415\u0422\u0415\u0422\u0415<\/strong> \u2013 p. 100<\/p>\n<p>\u00a0<\/p>\n<p><strong>GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u042f \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/strong> \u2013 \u0441\u0442\u0440. 102<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong style=\"font-size: 12.16px;\"><a name=\"art01\"><\/a>COMPUTER DISCOVERED MATHEMATICS: CONSTRUCTIONS OF MALFATTI SQUARES<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> By using the computer program \u201cDiscoverer\u201d we find 85 different geometric constructions of Malfatti squares. Of them 79 are new constructions, and the other 6 are old constructions.<br \/><em>Keywords:<\/em> Malfatti squares, geometric construction, triangle geometry, computer discovered mathematics, Euclidean geometry, \u201cDiscoverer\u201d<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Sava Grozdev, DSc.<br \/>University of Finance, Business and Entrepreneurship<br \/>Sofia, Bulgaria<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Dr. Hiroshi Okumura<br \/>Maebashi Gunma, Japan<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Deko Dekov, Assoc. Prof.<br \/>Stara Zagora, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong style=\"font-size: 12.16px;\"><span style=\"font-size: 12.16px;\"><a name=\"art02\"><\/a>\u0414\u0418\u0410\u0413\u041e\u041d\u0410\u041b\u041d\u0418 \u0422\u041e\u0427\u041a\u041e\u0412\u0418 \u041a\u041e\u041d\u0424\u0418\u0413\u0423\u0420\u0410\u0426\u0418\u0418. \u041f\u0420\u0410\u0412\u0418\u041b\u041e \u041d\u0410 \u0422\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u041a\u0410. \u0418\u041d\u0412\u0410\u0420\u0418\u0410\u041d\u0422\u0418<\/span><\/strong><\/p>\n<p>\u00a0<\/p>\n<p>Zdravko Lalchev, Irina Voutova<br \/>Sofia University<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u0435\u043d\u043e \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u0447\u043d\u043e \u043f\u0440\u043e\u0434\u044a\u043b\u0436\u0435\u043d\u0438\u0435 (\u0441 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u043d\u0438 \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430) \u043d\u0430 \u0438\u0434\u0435\u044f\u0442\u0430 \u0437\u0430 \u043b\u0438\u0446\u0435 \u0438 \u043e\u0431\u0435\u043c \u043e\u0442 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0438\u044f \u043a\u0443\u0440\u0441 \u043f\u043e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f. \u041f\u043e\u043a\u0430\u0437\u0430\u043d\u043e \u0435, \u0447\u0435 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438\u0442\u0435 \u0444\u0438\u0433\u0443\u0440\u0438 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u0438 \u043e\u043a\u0442\u0430\u0435\u0434\u044a\u0440 \u0441\u0430 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u0438\u0437\u0430\u0446\u0438\u0438 \u043d\u0430 \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u043d\u0438 \u0442\u043e\u0447\u043a\u043e\u0432\u0438 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438 \u0438 \u0447\u0435 \u0438\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u0438\u0442\u0435 \u043d\u0430 \u0442\u0435\u0437\u0438 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438 \u0441\u0430 \u0430\u043d\u0430\u043b\u043e\u0437\u0438 \u043d\u0430 \u043f\u043e\u043d\u044f\u0442\u0438\u044f\u0442\u0430 \u043b\u0438\u0446\u0435 \u043d\u0430 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u0438 \u043e\u0431\u0435\u043c \u043d\u0430 \u043e\u043a\u0442\u0430\u0435\u0434\u044a\u0440. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d \u0435 \u0435\u0434\u0438\u043d\u0435\u043d \u043f\u043e\u0434\u0445\u043e\u0434 \u043f\u0440\u0438 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044f\u0442\u0430 \u0437\u0430 \u201e\u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u043d\u0438\u201c \u0438\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u0438 \u0432 2-\u043c\u0435\u0440\u043d\u043e, 3-\u043c\u0435\u0440\u043d\u043e, 4-\u043c\u0435\u0440\u043d\u043e \u0438 n-\u043c\u0435\u0440\u043d\u043e (n &gt; 4) \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e. \u0421 \u0446\u0435\u043b \u0443\u043b\u0435\u0441\u043d\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u044f\u0442\u0430 \u0438 \u043e\u043f\u0440\u043e\u0441\u0442\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430\u0442\u0430 \u0441\u0430 \u0432\u044a\u0432\u0435\u0434\u0435\u043d\u0438 \u043a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u0438 \u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u0430 \u0441\u044a\u0449\u043e \u0442\u0430\u043a\u0430 \u0435 \u0438\u0437\u0432\u0435\u0434\u0435\u043d\u043e \u0438 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u043e \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043de \u043d\u0430 \u201e\u043f\u0440\u0430\u0432\u0438\u043b\u043e\u0442\u043e \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430\u201c.<br \/><em>Keywords:<\/em> n-dimensional space; coordinate; point, vector; diagonal configuration of points; determinant; invariant; triangle rule<\/p>\n<p>\u00a0<\/p>\n<p><strong>DIAGONAL CONFIGURATIONS OF POINTS. TRIANGLE RULE. INVARIANTS<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> Some new concepts such as diagonal configuration of points and its invariants are introduced in the present work. It is shown that the quadrilateral and the octahedron are concretization of a diagonal configuration of points and that the invariants of these configurations are analogues of the concepts of area of a quadrilateral and volume of an octahedron. The idea of invariants of diagonal configurations of points is consistently developed (an integrated approach is used) for 2-dimentional, 3-dimentional, 4-dimentional, n-dimentional (n&gt; 4) space. Compact symbols are introduced in order to facilitate the general conclusions and to simplify the demonstrations, also the \u201etriangle rule\u201c is deduced and consistently applied.<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Dr. Zdravko Lalchev<br \/>Faculty of Preschool and Primary Education<br \/>University of Sofia<br \/>Sofia, Bulgaria<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Irina Voutova, Assist. Prof.<br \/>Faculty of Mathematics and Informatics<br \/>University of Sofia<br \/>Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong style=\"font-size: 12.16px;\"><span style=\"font-size: 12.16px;\"><a name=\"art03\"><\/a>\u041e\u0421\u042a\u0429\u0415\u0421\u0422\u0412\u042f\u0412\u0410\u041d\u0415 \u041d\u0410 \u0412\u042a\u0422\u0420\u0415\u0428\u041d\u041e\u041f\u0420\u0415\u0414\u041c\u0415\u0422\u041d\u0418 \u0412\u0420\u042a\u0417\u041a\u0418 \u0412 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u2013 \u0422\u0420\u0418\u0413\u041e\u041d\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0418 \u0424\u0423\u041d\u041a\u0426\u0418\u0418 \u0418 \u041f\u0420\u041e\u0413\u0420\u0415\u0421\u0418\u0418<\/span><\/strong><\/p>\n<p>\u00a0<\/p>\n<p>\u0417\u0430\u0440\u0430 \u0414\u0430\u043d\u0430\u0438\u043b\u043e\u0432\u0430-\u0421\u0442\u043e\u0439\u043d\u043e\u0432\u0430, \u0420\u0435\u0433\u0438\u043e\u043d\u0430\u043b\u043d\u0438 \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e \u2013 \u041f\u043b\u043e\u0432\u0434\u0438\u0432<br \/>\u041f\u0435\u0442\u044a\u0440 \u0414\u0430\u043d\u0447\u0435\u0432, \u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u0423\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u2013 \u0421\u043e\u0444\u0438\u044f<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0441\u0430 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u0437\u0430 \u043e\u0441\u044a\u0449\u0435\u0441\u0442\u0432\u044f\u0432\u0430\u043d\u0435 \u043d\u0430 \u0432\u044a\u0442\u0440\u0435\u0448\u043d\u043e\u043f\u0440\u0435\u0434\u043c\u0435\u0442\u043d\u0438 \u0432\u0440\u044a\u0437\u043a\u0438 \u043c\u0435\u0436\u0434\u0443 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043f\u0440\u043e\u0433\u0440\u0435\u0441\u0438\u0438\u0442\u0435 \u0432 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0438\u044f \u043a\u0443\u0440\u0441 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430.<br \/><em>Keywords:<\/em> internal disciplinary connection; trigonometric function; arithmetic and geometric progression; problem solving<\/p>\n<p>\u00a0<\/p>\n<p><strong>REALIZATION OF INTERDISCIPLINARY CONNECTIONS IN MATHEMATICS TRAINING \u2013TRIGONOMETRIC FUNCTIONS AND PROGRESSIONS<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> Examples are shown in the present paper about the realization of interdisciplinary connections between trigonometric functions and progressions in high school mathematical curriculum.<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Zara Danailova-Stoynova<br \/>Regional Department of Education<br \/>Plovdiv, Bulgaria<\/p>\n<p>Mr. Peter Vassilev Danchev, Assist. Prof.<br \/>Technical University of Sofia<br \/>Sofia, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong style=\"font-size: 12.16px;\"><a name=\"art04\"><\/a>\u0420\u0410\u0412\u041d\u041e\u041b\u0418\u0426\u0415\u0412\u0418 \u0422\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u0426\u0418, \u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u0418 \u041e\u0422 \u0414\u0412\u0415 \u041f\u0420\u0415\u041e\u0411\u0420\u0410\u0417\u0423\u0412\u0410\u041d\u0418\u042f \u0412 \u0420\u0410\u0412\u041d\u0418\u041d\u0410\u0422\u0410 \u041d\u0410 \u0422\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u041a<\/strong><\/p>\n<p>\u0418\u0432\u0430\u043d \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432, \u0414\u0435\u044f\u043d \u0414\u0438\u043c\u0438\u0442\u0440\u043e\u0432, \u0411\u043e\u0440\u0438\u0441\u043b\u0430\u0432 \u0411\u043e\u0440\u0438\u0441\u043e\u0432<br \/>Mathematics High School \u2013 Lovech<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u0443\u0447\u0435\u043d\u0438\u0447\u0435\u0441\u043a\u0430 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u043f\u043e\u0434 \u0440\u044a\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e\u0442\u043e \u043d\u0430 \u0434\u043e\u0446. \u0434-\u0440 \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432. \u041d\u043e\u0432\u0438\u0442\u0435 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438 \u0432 \u043d\u0435\u044f \u043f\u043e\u043b\u0443\u0447\u0438\u0445\u0430 \u043e\u0442\u043b\u0438\u0447\u043d\u0430 \u043e\u0446\u0435\u043d\u043a\u0430 \u043f\u043e \u0432\u0440\u0435\u043c\u0435 \u043d\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435\u0442\u043e \u0439 \u0432 \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0438\u044f \u043a\u043e\u043d\u043a\u0443\u0440\u0441 \u201e\u041c\u0435\u0442\u043e\u0434\u043e\u043b\u043e\u0433\u0438\u044f \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u0442\u043e\u201d \u043f\u0440\u0435\u0437 2018 \u0433. \u0438 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u043f\u043e\u043b\u0443\u0447\u0438 \u043f\u044a\u0440\u0432\u0430 \u043d\u0430\u0433\u0440\u0430\u0434\u0430. \u0422\u044f \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u0435\u0434\u043d\u0430 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0437\u0430 \u043b\u0438\u0446\u0430 \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0438 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438 \u043e\u0442 \u0441\u0435\u043a\u0443\u0449\u0438 \u0432 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430. \u041d\u0430\u043c\u0435\u0440\u0435\u043d\u0430 \u0435 \u043e\u0431\u0449\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0437\u0430 \u043b\u0438\u0446\u0435\u0442\u043e \u043d\u0430 \u0435\u0434\u0438\u043d \u043e\u0442 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438\u0442\u0435. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438 \u0441\u0430 \u043b\u0438\u0446\u0430\u0442\u0430 \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438 \u0447\u0440\u0435\u0437 \u0438\u0437\u043e\u0442\u043e\u043c\u0438\u0447\u043d\u043e\u0442\u043e \u0438 \u0438\u0437\u043e\u0433\u043e\u043d\u0430\u043b\u043d\u043e\u0442\u043e \u0441\u044a\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u044f \u0432 \u0440\u0430\u0432\u043d\u0438\u043d\u0430\u0442\u0430 \u043d\u0430 \u0434\u0430\u0434\u0435\u043d \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a. \u0418\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d \u0435 \u0438 \u0432\u044a\u043f\u0440\u043e\u0441\u044a\u0442 \u0437\u0430 \u0440\u0430\u0432\u043d\u043e\u043b\u0438\u0446\u0435\u0432\u043e\u0441\u0442 \u043d\u0430 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u0442\u0435 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0441 \u043f\u043e\u0440\u0430\u0436\u0434\u0430\u0449\u0438\u0442\u0435 \u0433\u0438 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438.<br \/><em>Keywords:<\/em> triangle; area; isotomic transformation; isogonal transformation; polynomial root<\/p>\n<p>\u00a0<\/p>\n<p><strong>TRIANGLES WITH EQUAL AREAS, GENERATED BY TWO TRANSFORMATIONS IN THE TRIANGLE PLANE<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract:<\/strong> The paper is an elaboration by high school students under the scientific advices of Assoc. Prof. Veselin Nenkov, PhD. The new results in it were estimated highly during its presentation at the International competition \u201cMethodology and Information Technologies in Education\u201d in 2018 and the work was awarded first prize. It is dedicated to a well-known problem for triangle and quadrilateral areas determined by triangle secants. A general formula is found for the area of one of the triangles. The areas of triangles are determined when obtained by isotomic and isogonal transformations in the plane of a given triangle. What is investigated is the question for equal areas of the obtained triangles and the generating ones.<\/p>\n<p>\u00a0<\/p>\n<p>Mr. Ivan Stefanov, Student <br \/>Mr. Deyan Dimitrov, Student<br \/>Mr. BorislavBorisov, Student<br \/>Mathematics High School \u2013 Lovech<br \/>Lovech, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong style=\"font-size: 12.16px;\"><a name=\"art05\"><\/a>\u0412\u0420\u042a\u0417\u041a\u0418 \u041c\u0415\u0416\u0414\u0423 \u0417\u0410\u0411\u0415\u041b\u0415\u0416\u0418\u0422\u0415\u041b\u041d\u0418 \u0422\u041e\u0427\u041a\u0418 \u0412 \u0427\u0415\u0422\u0418\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u041a\u0410<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>\u0421\u0442\u0430\u043d\u0438\u0441\u043b\u0430\u0432 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432, \u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u2013 \u0421\u043e\u0444\u0438\u044f<br \/>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0432\u0440\u044a\u0437\u043a\u0438 \u043c\u0435\u0436\u0434\u0443 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \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. \u041d\u0430\u043c\u0435\u0440\u0435\u043d\u0438 \u0441\u0430 \u0442\u0440\u0438 \u0437\u0430\u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0435\u043b\u043d\u0438 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438 \u0438 \u0434\u0432\u0435 \u0437\u0430\u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0435\u043b\u043d\u0438 \u043f\u0440\u0430\u0432\u0438, \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u0449\u0438 \u043d\u044f\u043a\u043e\u0438 \u043e\u0442 \u0442\u0435\u0437\u0438 \u0442\u043e\u0447\u043a\u0438.<br \/><em>Keywords:<\/em> quadrilateral; notable point; line; circle<\/p>\n<p>\u00a0<\/p>\n<p><strong>CONNECTIONS AMONG NOTABLE POINTS IN THE QUADRILATERAL<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> The paper considers some geometric connections among different notable points in the quadrilateral. What are obtained are three notable circles and two notable lines which contain some of these points.<\/p>\n<p>\u00a0<\/p>\n<p>Mr. Stanislav Stefanov<br \/>Technical University Sofia<br \/>Sofia, Bulgaria<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof.<br \/>Lovech, Bulgaria<\/p>\n<p style=\"text-align: right;\">\u00a0<a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong><span style=\"font-size: 12.16px;\"><a name=\"art06\"><\/a>\u0422\u0420\u041e\u0419\u041a\u0418 \u0426\u0415\u041d\u0422\u0420\u0410\u041b\u041d\u0418 \u041a\u041e\u041d\u0418\u0427\u041d\u0418 \u0421\u0415\u0427\u0415\u041d\u0418\u042f \u041f\u0420\u0415\u0417 \u041f\u041e\u0421\u0422\u041e\u042f\u041d\u041d\u0410 \u0422\u041e\u0427\u041a\u0410 \u0412\u042a\u0420\u0425\u0423 \u041a\u041e\u041d\u0418\u0427\u041d\u041e \u0421\u0415\u0427\u0415\u041d\u0418\u0415<\/span><\/strong><\/p>\n<p>\u00a0<\/p>\n<p>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0438\u0441\u0448\u0435 \u0443\u0447\u0438\u043b\u0438\u0449\u0435 \u043f\u043e \u0437\u0430\u0441\u0442\u0440\u0430\u0445\u043e\u0432\u0430\u043d\u0435 \u0438 \u0444\u0438\u043d\u0430\u043d\u0441\u0438 \u2013 \u0421\u043e\u0444\u0438\u044f<br \/>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0435\u0434\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0437\u0430 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438 \u043f\u0440\u0435\u0437 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430 \u0442\u043e\u0447\u043a\u0430 \u0432 \u0440\u0430\u0432\u043d\u0438\u043d\u0430\u0442\u0430 \u043d\u0430 \u0434\u0430\u0434\u0435\u043d \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a.<br \/><em>Keywords:<\/em> triangle; center; centroid; circum curve; Euler line<\/p>\n<p>\u00a0<\/p>\n<p><strong>CENTRAL CONIC TRIPLETS THROUGH A FIXED POINT ON A FIXED CONIC<\/strong><\/p>\n<p>\u00a0<\/p>\n<p><strong>Abstract:<\/strong> The paper presents a generalization of a problem for circles through a fixed point in the plane of a given triangle.<\/p>\n<p>\u00a0<\/p>\n<p>Prof. Sava Grozdev, DSc.<br \/>University of Finance, Business and Entrepreneurship<br \/>Sofia, Bulgaria<\/p>\n<p>\u00a0<\/p>\n<p>Dr. Veselin Nenkov, Assoc. Prof.<br \/>Lovech, Bulgaria<\/p>\n<p style=\"text-align: right;\"><a href=\"#top\">\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n<hr \/>\n<p style=\"text-align: right;\">\u00a0<\/p>","protected":false},"excerpt":{"rendered":"<p>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u00a0 EDITORIAL \/ \u041a\u042a\u041c \u0427\u0418\u0422\u0410\u0422\u0415\u041b\u042f \u2013 \u0441\u0442\u0440. 7\u00a0\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \u00a0 EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418Computer Discovered Mathematics: Constructions of Malfatti Squares [\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043e\u0442\u043a\u0440\u0438\u0442\u0430 \u043e\u0442 \u043a\u043e\u043c\u043f\u044e\u0442\u0440\u0438: \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438 \u043d\u0430 \u043a\u0432\u0430\u0434\u0430\u0442\u0438\u0442\u0435 \u043d\u0430 \u041c\u0430\u043b\u0444\u0430\u0442\u0438] \/ Sava Grozdev, Hiroshi Okumura, Deko Dekov \u2013 \u0441\u0442\u0440. 10\u00a0\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442\u00a0\u00a0 \u00a0 \u0414\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u043d\u0438 \u0442\u043e\u0447\u043a\u043e\u0432\u0438 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438. \u041f\u0440\u0430\u0432\u0438\u043b\u043e \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430. \u0418\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u0438 [Diagonal [&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":[3614],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>&quot;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&quot;, \u043a\u043d\u0438\u0436\u043a\u0430 1, \u0433\u043e\u0434\u0438\u043d\u0430 LXI, 2018 - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/bel.azbuki.bg\/en\/matematics\/matharticles2016-3\/1-lxi-2018\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"&quot;\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430&quot;, \u043a\u043d\u0438\u0436\u043a\u0430 1, \u0433\u043e\u0434\u0438\u043d\u0430 LXI, 2018 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u00a0 EDITORIAL \/ \u041a\u042a\u041c \u0427\u0418\u0422\u0410\u0422\u0415\u041b\u042f \u2013 \u0441\u0442\u0440. 7\u00a0\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \u00a0 EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418Computer Discovered Mathematics: Constructions of Malfatti Squares [\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043e\u0442\u043a\u0440\u0438\u0442\u0430 \u043e\u0442 \u043a\u043e\u043c\u043f\u044e\u0442\u0440\u0438: \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438 \u043d\u0430 \u043a\u0432\u0430\u0434\u0430\u0442\u0438\u0442\u0435 \u043d\u0430 \u041c\u0430\u043b\u0444\u0430\u0442\u0438] \/ Sava Grozdev, Hiroshi Okumura, Deko Dekov \u2013 \u0441\u0442\u0440. 10\u00a0\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442\u00a0\u00a0 \u00a0 \u0414\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u043d\u0438 \u0442\u043e\u0447\u043a\u043e\u0432\u0438 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438. \u041f\u0440\u0430\u0432\u0438\u043b\u043e \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430. \u0418\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u0438 [Diagonal [&hellip;]\" \/>\n<meta property=\"og:url\" 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\u041a\u042a\u041c \u0427\u0418\u0422\u0410\u0422\u0415\u041b\u042f \u2013 \u0441\u0442\u0440. 7\u00a0\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442 \u00a0 EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418Computer Discovered Mathematics: Constructions of Malfatti Squares [\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u043e\u0442\u043a\u0440\u0438\u0442\u0430 \u043e\u0442 \u043a\u043e\u043c\u043f\u044e\u0442\u0440\u0438: \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438 \u043d\u0430 \u043a\u0432\u0430\u0434\u0430\u0442\u0438\u0442\u0435 \u043d\u0430 \u041c\u0430\u043b\u0444\u0430\u0442\u0438] \/ Sava Grozdev, Hiroshi Okumura, Deko Dekov \u2013 \u0441\u0442\u0440. 10\u00a0\u041e\u0442\u0432\u043e\u0440\u0438 \u043f\u044a\u043b\u043d\u0438\u044f \u0442\u0435\u043a\u0441\u0442\u00a0\u00a0 \u00a0 \u0414\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u043d\u0438 \u0442\u043e\u0447\u043a\u043e\u0432\u0438 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438. \u041f\u0440\u0430\u0432\u0438\u043b\u043e \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430. \u0418\u043d\u0432\u0430\u0440\u0438\u0430\u043d\u0442\u0438 [Diagonal [&hellip;]","og_url":"https:\/\/bel.azbuki.bg\/en\/matematics\/matharticles2016-3\/1-lxi-2018\/","og_site_name":"\u0410\u0437-\u0431\u0443\u043a\u0438","article_publisher":"https:\/\/www.facebook.com\/Azbuki55\/","article_published_time":"2018-03-01T09:24:20+00:00","article_modified_time":"2019-06-18T18:58:27+00:00","og_image":[{"url":"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png"}],"twitter_card":"summary_large_image","twitter_misc":{"Written by":"","Est. reading time":"3 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