{"id":38476,"date":"2013-11-03T14:16:00","date_gmt":"2013-11-03T11:16:00","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/mathinfo062013\/"},"modified":"2019-06-24T17:33:15","modified_gmt":"2019-06-24T14:33:15","slug":"mathinfo062013","status":"publish","type":"post","link":"https:\/\/philosophy.azbuki.bg\/en\/matematics\/matharticles\/mathinfo062013\/","title":{"rendered":"Mathematics and Informatics, Number 6\/2013, Volume 56"},"content":{"rendered":"

 <\/a>\u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS<\/strong><\/p>\n

Five New Proofs of One Trigonometric Inequality in the Triangle
\u041f\u0435\u0442 \u043d\u043e\u0432\u0438 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430 \u043d\u0430 \u0435\u0434\u043d\u043e \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0432 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 <\/a>\/
\u0160efket Arslanagi\u0107, Alija Muminagi\u0107 \/ \u0428\u0435\u0444\u043a\u0435\u0442 \u0410\u0440\u0441\u043b\u0430\u043d\u0430\u0433\u0438\u0447, \u0410\u043b\u0438\u044f \u041c\u0443\u043c\u0438\u043d\u0430\u0433\u0438\u0447<\/em> – 505
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\u0415\u0434\u043d\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0437\u0430 \u0442\u0440\u0430\u043f\u0435\u0446
A Generalization of an Inequality for Trapezoid <\/a>\/
\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Veselin Nenkov<\/em> – 509
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\u041f\u0440\u043e\u0435\u043a\u0442\u0438\u0432\u043d\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u043d\u0438 \u043a\u0440\u0438\u0432\u0438, \u043a\u043e\u043d\u0438\u0447\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0438 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u041f\u0430\u0441\u043a\u0430\u043b
Projective Algebraic Curves, Conics and Pascal Theorem <\/a>\/
\u0416\u0438\u0432\u043a\u043e \u0416\u0435\u043b\u0435\u0432 \/ Zhivko Zhelev<\/em> – 514
Log in to read the full text<\/a><\/p>\n

 <\/p>\n

\u0413\u0440\u0430\u0444\u0438\u0447\u043d\u043e \u0438 \u0447\u0438\u0441\u043b\u0435\u043d\u043e \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440
Graphical and Numerical Computer-Aided Solutions of Equations and Inequalities <\/a>\/
\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0414\u0435\u043a\u043e \u0414\u0435\u043a\u043e\u0432 \/ Sava Grozdev, Deko Dekov<\/em> – 522
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\u041e\u0442\u043d\u043e\u0441\u043d\u043e \u043d\u044f\u043a\u043e\u0438 \u0438\u0437\u0445\u043e\u0434\u043d\u0438 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043f\u0440\u0438 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0435\u0434\u043d\u0430 \u0435\u0432\u0440\u0438\u0441\u0442\u0438\u0447\u043d\u043e \u043e\u0440\u0438\u0435\u043d\u0442\u0438\u0440\u0430\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u043e\u0442 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438
About Certain Foundations in the Design of a Heuristic-Oriented System of Geometric Problems <\/a>\/
\u041d\u0438\u043d\u0430 \u0418\u0432\u0430\u043d\u043e\u0432\u0430 \/ Nina Ivanova – <\/em>529
Log in to read the full text<\/a><\/p>\n

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\u0418\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u0444\u0440\u0430\u043a\u0442\u0430\u043b\u043d\u0438 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438 \u0447\u0440\u0435\u0437 Geogebra \u0437\u0430 \u0445\u0438\u0431\u0440\u0438\u0434\u0435\u043d \u0443\u0447\u0435\u0431\u0435\u043d \u043f\u0440\u043e\u0446\u0435\u0441
Integration of Geometric Fractal Structures by Geogebra for a Blended Learning Process <\/a>\/
\u041c\u0430\u0433\u0434\u0430\u043b\u0435\u043d\u0430 \u041f\u0435\u0442\u043a\u043e\u0432\u0430 \/ Magdalena Petkova<\/em> – 541
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\u0421\u0442\u0440\u0430\u0442\u0435\u0433\u0438\u0438 \u0437\u0430 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u043d\u0435 \u0432 \u0441\u0440\u0435\u0434\u0430 \u0437\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435
Teaching Strategies in E-Learning Environment <\/a>\/
\u0412\u0435\u043d\u0446\u0438\u0441\u043b\u0430\u0432 \u0414\u0436\u0430\u043c\u0431\u0430\u0437\u043e\u0432 \/ Vencislav Dzambazov<\/em> – 562
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\u041c\u0430\u0448\u0438\u043d\u043d\u0430 \u0430\u0440\u0438\u0442\u043c\u0435\u0442\u0438\u043a\u0430 \u0432 \u0447\u0430\u0441\u043e\u0432\u0435\u0442\u0435 \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430
Machine Arithmetic in Informatics Classes <\/a>\/
\u041f\u043b\u0430\u043c\u0435\u043d \u041f\u0435\u043d\u0435\u0432 \/ Plamen Penev<\/em> – 569
Log in to read the full text<\/a><\/p>\n

 <\/p>\n

\u041a\u0440\u0438\u0442\u0435\u0440\u0438\u0438 \u0437\u0430 \u043e\u0446\u0435\u043d\u043a\u0430 \u043d\u0430 \u043f\u0440\u043e\u0435\u043a\u0442\u0438 \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 \u0432 \u043f\u043b\u0430\u0442\u0444\u043e\u0440\u043c\u0430\u0442\u0430 e-Twinnng
Criteria for Evaluation of Information Technology Projects in the e-Twinning platform <\/a>\/
\u0414\u0430\u043d\u0438\u0435\u043b\u0430 \u0414\u0438\u043c\u0438\u0442\u0440\u043e\u0432\u0430 \/ Daniela Dimitrova<\/em> – 579
Log in to read the full text<\/a><\/p>\n

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\u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418 \/ CONTEST PROBLEMS<\/strong>
\u0420\u0443\u0431\u0440\u0438\u043a\u0430\u0442\u0430 \u0441\u0435 \u0432\u043e\u0434\u0438 \u043e\u0442 \u0434-\u0440 \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \u0438 \u0434-\u0440 \u0416\u0438\u0432\u043a\u043e \u0416\u0435\u043b\u0435\u0432<\/p>\n

<\/em>Contest Problems of this Issue
Contest Problems of the Issue – 595<\/p>\n

\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, 2013
Solutions of the Contest Problems from issue 1, 2013 – 596<\/p>\n


\u0413\u041e\u0414\u0418\u0428\u041d\u041e \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ ANNUAL CONTENT<\/strong> – 599<\/p>\n


\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\u201d \u0427\u0415\u0422\u0415\u0422\u0415 \/ <\/strong>
READ IN THE LATEST ISSUES OF \u201eAZ BUKI\u201d JOURNALS<\/strong> – 603<\/p>\n


\u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415 \/ GUIDE FOR AUTHORS<\/strong> – 605<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a><\/strong>NEW PROOFS OF ONE TRIGONOMETRIC INEQUALITY IN THE TRIANGLE<\/p>\n

<\/strong>\u0160efket Arslanagi\u0107, Alija Muminagi\u0107<\/p>\n

<\/strong>Abstract.<\/strong> The paper considers five proofs of the ineqaulity.

Keywords<\/i>: <\/strong>trigonometric inequality, triangle, proof
<\/p>\n

\u041f\u0415\u0422 \u041d\u041e\u0412\u0418 \u0414\u041e\u041a\u0410\u0417\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u0410 \u041d\u0410 \u0415\u0414\u041d\u041e \u0422\u0420\u0418\u0413\u041e\u041d\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u041e \u041d\u0415\u0420\u0410\u0412\u0415\u041d\u0421\u0422\u0412\u041e \u0412 \u0422\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u041a\u0410<\/p>\n

<\/strong>\u0428\u0435\u0444\u043a\u0435\u0442 \u0410\u0440\u0441\u043b\u0430\u043d\u0430\u0433\u0438\u0447, \u0410\u043b\u0438\u044f \u041c\u0443\u043c\u0438\u043d\u0430\u0433\u0438\u0447<\/strong><\/p>\n

Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u043f\u0435\u0442 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430 \u043d\u0430 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e\u0442\u043e .<\/p>\n

\u0160efket Arslanagi\u0107
<\/strong>Professor, Doctor in Mathematics
Faculty of Mathematics and Natural Sciences
University of Sarajevo
Sarajevo, Bosna and Herzegovina<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a>\u0415\u0414\u041d\u041e \u041d\u0415\u0420\u0410\u0412\u0415\u041d\u0421\u0422\u0412\u041e \u0417\u0410 \u0422\u0420\u0410\u041f\u0415\u0426<\/p>\n

<\/strong>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<\/p>\n

<\/strong>Abstract.<\/strong> \u0422\u0430\u0437\u0438 \u0431\u0435\u043b\u0435\u0436\u043a\u0430 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u0435\u0434\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0437\u0430 \u0442\u0440\u0430\u043f\u0435\u0446 \u043e\u0442 \u0441\u043f. \u201e\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\u201c, 2000 \u0433.

Keywords<\/i>: convex quadrilateral, square, rhombus, trapezoid, area.
<\/p>\n

A GENERALIZATION OF AN INEQUALITY FOR TRAPEZOID<\/p>\n

<\/strong>Abstract.<\/strong> The present note is dedicated to a generalization of a problem from \u201eMathematics and Informatics\u201c journal, 2000. 

Veselin Nenkov
<\/strong>PhD, Associated Professor
Technical College Lovech<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a> \u041f\u0420\u041e\u0415\u041a\u0422\u0418\u0412\u041d\u0418 \u0410\u041b\u0413\u0415\u0411\u0420\u0418\u0427\u041d\u0418 \u041a\u0420\u0418\u0412\u0418, \u041a\u041e\u041d\u0418\u0427\u041d\u0418 \u0421\u0415\u0427\u0415\u041d\u0418\u042f \u0418 \u0422\u0415\u041e\u0420\u0415\u041c\u0410\u0422\u0410 \u041d\u0410 \u041f\u0410\u0421\u041a\u0410\u041b<\/p>\n

<\/strong>\u0416\u0438\u0432\u043a\u043e \u0416\u0435\u043b\u0435\u0432<\/p>\n

<\/strong>Abstract. <\/strong>\u0422\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u041f\u0430\u0441\u043a\u0430\u043b \u0435 \u043e\u0441\u043d\u043e\u0432\u0435\u043d \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442 \u0432 \u043a\u043b\u0430\u0441\u0438\u0447\u0435\u0441\u043a\u0430\u0442\u0430 \u043f\u0440\u043e\u0435\u043a\u0442\u0438\u0432\u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u043d\u0430 \u043a\u043e\u043d\u0438\u0447\u043d\u0438\u0442\u0435 \u0441\u0435\u0447\u0435\u043d\u0438\u044f. \u0427\u0440\u0435\u0437 \u043c\u0435\u0442\u043e\u0434\u0438\u0442\u0435 \u043d\u0430 \u0441\u044a\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u0442\u0430 \u0438\u0437\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u2013 \u0434\u044f\u043b \u043e\u0442 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u043d\u0430\u0442\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f, \u0437\u0430\u043d\u0438\u043c\u0430\u0432\u0430\u0449 \u0441\u0435 \u0441 \u043d\u0430\u043c\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0431\u0440\u043e\u044f \u043d\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438 \u043e\u0431\u0435\u043a\u0442\u0438 \u0432 \u0434\u0430\u0434\u0435\u043d\u043e \u043c\u043d\u043e\u0433\u043e\u043e\u0431\u0440\u0430\u0437\u0438\u0435, \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u0432\u0430\u0449\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u0443\u0441\u043b\u043e\u0432\u0438\u044f \u2013 \u0441\u0430 \u0440\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u043a\u0430\u043a\u0442\u043e \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u041f\u0430\u0441\u043a\u0430\u043b, \u0442\u0430\u043a\u0430 \u0438 \u043d\u044f\u043a\u043e\u0438 \u0434\u0440\u0443\u0433\u0438 \u0444\u0430\u043a\u0442\u0438 \u043e\u0442 \u043f\u0440\u043e\u0435\u043a\u0442\u0438\u0432\u043d\u0430\u0442\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f.

Keywords:<\/i>  Enumerative geometry, intersection theory, Bezout theorem, Pascal theorem.

PROJECTIVE ALGEBRAIC CURVES, CONICS AND PASCAL THEOREM<\/p>\n

<\/strong>Abstract.<\/strong>  The Pascal theorem is a key result in the classic Projective geometry of conics. The paper considers the Pascal theorem and some other facts from Projective geometry by means of the methods of the contemporary Enumerative geometry \u2013 a part of the Algebraic geometry dealing with the number of various geometric objects under different conditions in a given variety.<\/p>\n

Zhivko Zhelev
<\/strong>PhD, Assistant Professor
Department of Informatics & Mathematics
Faculty of Economics
Trakia University 
Stara Zagora, Bulgaria<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a>\u0413\u0420\u0410\u0424\u0418\u0427\u041d\u041e \u0418 \u0427\u0418\u0421\u041b\u0415\u041d\u041e \u0420\u0415\u0428\u0410\u0412\u0410\u041d\u0415 \u041d\u0410 \u0423\u0420\u0410\u0412\u041d\u0415\u041d\u0418\u042f \u0418 \u041d\u0415\u0420\u0410\u0412\u0415\u041d\u0421\u0422\u0412\u0410 \u0421 \u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420<\/p>\n

<\/strong>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0414\u0435\u043a\u043e \u0414\u0435\u043a\u043e\u0432<\/p>\n

<\/strong>Abstract. <\/strong>\u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u043c\u0435\u0442\u043e\u0434\u0438 \u0437\u0430 \u0433\u0440\u0430\u0444\u0438\u0447\u043d\u043e \u0438 \u0447\u0438\u0441\u043b\u0435\u043d\u043e \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440. \u0414\u0438\u0441\u043a\u0443\u0442\u0438\u0440\u0430 \u0441\u0435 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430\u0442\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u201e\u0413\u0440\u0430\u0444\u201c \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0442\u0435\u0437\u0438 \u0437\u0430\u0434\u0430\u0447\u0438.

Keywords<\/i>: computer-aided solution, equation, inequality, table, Graph

GRAPHICAL AND NUMERICAL COMUTER-AIDED SOLUTIONS OF EQUATIONS AND INEQUALITIES<\/p>\n

<\/strong>Abstract.<\/strong> The paper considers methods for graphical and numerical computer-aided solutions of equations and inequalities. It discusses the application of the computer program Graph to such problems.<\/p>\n

Sava Grozdev
<\/strong>Professor, Doctor in Mathematics, DSc in Pedagogy
Institute of Mathematics and Informatics \u2013 BAS
Sofia, Bulgaria<\/p>\n

Deko Dekov
<\/strong>Associated Professor, PhD in Mathematics
Stara Zagora<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a> \u041e\u0422\u041d\u041e\u0421\u041d\u041e \u041d\u042f\u041a\u041e\u0418 \u0418\u0417\u0425\u041e\u0414\u041d\u0418 \u041f\u041e\u041b\u041e\u0416\u0415\u041d\u0418\u042f \u041f\u0420\u0418 \u041a\u041e\u041d\u0421\u0422\u0420\u0423\u0418\u0420\u0410\u041d\u0415\u0422\u041e \u041d\u0410 \u0415\u0414\u041d\u0410 \u0415\u0412\u0420\u0418\u0421\u0422\u0418\u0427\u041d\u041e \u041e\u0420\u0418\u0415\u041d\u0422\u0418\u0420\u0410\u041d\u0410 \u0421\u0418\u0421\u0422\u0415\u041c\u0410 \u041e\u0422 \u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/p>\n

<\/strong>\u041d\u0438\u043d\u0430 \u0418\u0432\u0430\u043d\u043e\u0432\u0430<\/p>\n

<\/strong>Abstract.<\/strong> \u0417\u0430\u0449\u043e \u0442\u0440\u044f\u0431\u0432\u0430 \u0434\u0430 \u043d\u0430\u0441\u044a\u0440\u0447\u0430\u0432\u0430\u043c\u0435 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435 \u0434\u0430 \u0440\u0430\u0437\u0433\u0440\u044a\u0449\u0430\u0442 \u0441\u0432\u043e\u044f \u0435\u0432\u0440\u0438\u0441\u0442\u0438\u0447\u0435\u043d \u0438 \u0442\u0432\u043e\u0440\u0447\u0435\u0441\u043a\u0438 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b? \u041a\u043e\u0433\u0430 \u0438 \u043a\u0430\u043a \u0434\u0430 \u0440\u0430\u0437\u0432\u0438\u0432\u0430\u043c\u0435 \u0443\u043c\u0435\u043d\u0438\u044f\u0442\u0430 \u0438\u043c \u0434\u0430 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u0442 \u043f\u0440\u0438\u0439\u043e\u043c\u0430 \u043d\u0430 \u0434\u043e\u043f\u044a\u043b\u043d\u0438\u0442\u0435\u043b\u043d\u0438\u0442\u0435 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u043e\u0442\u043e \u043c\u0443 \u043d\u0430 \u0441\u043f\u0435\u0446\u0438\u0430\u043b\u043d\u0430 \u0435\u0432\u0440\u0438\u0441\u0442\u0438\u043a\u0430? \u041a\u043e\u0438 \u0441\u0430 \u0438\u0437\u0445\u043e\u0434\u043d\u0438\u0442\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f, \u0441\u0432\u044a\u0440\u0437\u0430\u043d\u0438 \u0441 \u0438\u0437\u0433\u0440\u0430\u0436\u0434\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0434\u0438\u0434\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0446\u0435\u043b\u0435\u0441\u044a\u043e\u0431\u0440\u0430\u0437\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438, \u043e\u0431\u0441\u043b\u0443\u0436\u0432\u0430\u0449\u0430 \u043e\u0432\u043b\u0430\u0434\u044f\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0442\u043e\u0437\u0438 \u043f\u0440\u0438\u0439\u043e\u043c? \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0438 \u043f\u043e\u0434\u043a\u0440\u0435\u043f\u0435\u043d\u0438 \u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u0432\u044a\u0437\u0433\u043b\u0435\u0434\u0438\u0442\u0435 \u043d\u0430 \u0430\u0432\u0442\u043e\u0440\u0430 \u043e\u0442\u043d\u043e\u0441\u043d\u043e \u043f\u043e\u0441\u0442\u0430\u0432\u0435\u043d\u0438\u0442\u0435 \u0438 \u0434\u0440\u0443\u0433\u0438, \u0442\u044f\u0441\u043d\u043e \u0441\u0432\u044a\u0440\u0437\u0430\u043d\u0438 \u0441 \u0442\u044f\u0445 \u0432\u044a\u043f\u0440\u043e\u0441\u0438. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438 \u0441\u0430 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u0437\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0442\u0438\u0437\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f\u0442\u0430, \u043a\u043e\u0438\u0442\u043e \u043e\u0431\u0438\u043a\u043d\u043e\u0432\u0435\u043d\u043e \u043d\u0430\u0440\u0438\u0447\u0430\u043c\u0435 \u0434\u043e\u043f\u044a\u043b\u043d\u0438\u0442\u0435\u043b\u043d\u0438 \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f.

Keywords:<\/i> heuristics, heuristic problem, additional construction, auxiliary elements

ABOUT CERTAIN FOUNDATIONS IN THE DESIGN OF A HEURISTIC-ORIENTED SYSTEM OF GEOMETRIC PROBLEMS<\/p>\n

<\/strong>Abstract.<\/strong> Why should we encourage the students to unleash their heuristic and creative potential? When and how to develop their skills in applying the method of additional constructions as a special heuristics? Which are the foundations related to the development of an appropriate didactic problem system, serving mastery of this method? The article shows the author\u2019s views by examples on the presented and other related problems. Reasons for systematic actions are given, which are usually called additional constructions.

Nina Ivanova
<\/strong>Department of Mathematics and Computer 
Science Teaching Methodology
Plovdiv University \u201ePaisii Hiledarski\u201c<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a> \u0418\u041d\u0422\u0415\u0413\u0420\u0418\u0420\u0410\u041d\u0415 \u041d\u0410 \u0413\u0415\u041e\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0418 \u0424\u0420\u0410\u041a\u0422\u0410\u041b\u041d\u0418 \u041a\u041e\u041d\u0421\u0422\u0420\u0423\u041a\u0426\u0418\u0418 \u0427\u0420\u0415\u0417 GEOGEBRA \u0417\u0410 \u0425\u0418\u0411\u0420\u0418\u0414\u0415\u041d \u0423\u0427\u0415\u0411\u0415\u041d \u041f\u0420\u041e\u0426\u0415\u0421<\/p>\n

<\/strong>\u041c\u0430\u0433\u0434\u0430\u043b\u0435\u043d\u0430 \u041f\u0435\u0442\u043a\u043e\u0432\u0430<\/p>\n

<\/strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u043f\u0440\u0430\u0432\u0438 \u0430\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u0441\u044a\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0442\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435, \u043a\u043e\u0435\u0442\u043e \u043f\u0440\u044f\u043a\u043e \u0437\u0430\u0432\u0438\u0441\u0438 \u043e\u0442 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0447\u043d\u043e\u0442\u043e \u0443\u0441\u044a\u0432\u044a\u0440\u0448\u0435\u043d\u0441\u0442\u0432\u0430\u043d\u0435. \u0418\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0438\u044f\u0442 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b \u043d\u0430 \u0432\u0441\u0438\u0447\u043a\u0438 \u043d\u0438\u0432\u0430 \u0441\u043b\u0435\u0434\u0432\u0430 \u0434\u0430 \u0431\u044a\u0434\u0435 \u0430\u0434\u0430\u043f\u0442\u0438\u0440\u0430\u043d \u043a\u044a\u043c \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0438\u0442\u0435 \u043d\u0430 \u043d\u043e\u0432\u043e\u0442\u043e \u043f\u043e\u043a\u043e\u043b\u0435\u043d\u0438\u0435, \u043a\u044a\u043c \u043f\u043e\u0432\u0438\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u043d\u0430\u043d\u0438\u044f\u0442\u0430 \u0438 \u0443\u043c\u0435\u043d\u0438\u044f\u0442\u0430 \u0447\u0440\u0435\u0437 \u043a\u043e\u043c\u0431\u0438\u043d\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438 \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0438 (\u0432\u043a\u043b. GeoGebra) \u0438 \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0444\u0440\u0430\u043a\u0442\u0430\u043b\u043d\u0438 \u043e\u0431\u0435\u043a\u0442\u0438 \u0441 \u0442\u044a\u0440\u0441\u0435\u043d\u0435 \u043d\u0430 \u0432\u0440\u044a\u0437\u043a\u0438 \u043c\u0435\u0436\u0434\u0443 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0430\u0442\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u0438 \u0444\u0440\u0430\u043a\u0442\u0430\u043b\u043d\u0430\u0442\u0430. \u041f\u043e\u043a\u0430\u0437\u0430\u043d\u0438 \u0441\u0430 \u043d\u044f\u043a\u043e\u043b\u043a\u043e \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0435\u043d\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u0441 \u0432\u043a\u043b\u044e\u0447\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u0430\u0441\u043e\u0447\u0432\u0430\u0449\u0438 \u0432\u044a\u043f\u0440\u043e\u0441\u0438, \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u0430\u043d\u0430\u043b\u0438\u0437 \u0438 \u0438\u0437\u0432\u043b\u0438\u0447\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u043a\u043e\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438, \u043a\u0430\u043a\u0442\u043e \u0438 \u043f\u043e\u0441\u0442\u0440\u043e\u044f\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0441\u043b\u0435\u0434\u0432\u0430\u0449\u0438 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u0446\u0438\u043e\u043d\u043d\u0438 \u043d\u0438\u0432\u0430 \u043d\u0430 \u0444\u0440\u0430\u043a\u0442\u0430\u043b\u043d\u0438 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u0438. <\/p>\n

Keyword<\/i>: fractal, GeoGebra, blended learning, Mathematics<\/p>\n

INTEGRATION OF GEOMETRIC FRACTAL STRUCTURES BY GEOGEBRA FOR A BLENDED LEARNING PROCESS <\/p>\n

<\/strong><\/span>Abstract. <\/i><\/strong>The paper analyzes contemporary teaching, which depends directly on technological improvement. The learning material at all levels should be adapted to the interests of the new generation, the increase of knowledge and skills combining various computer products (including GeoGebra) and studying fractal objects by looking for connections between elementary and fractal geometry. Several elaborated examples are presented including purposeful questions, tasks for analysis and deduction of regularities, but also constructing subsequent integration levels of fractal structures.<\/p>\n

Magdalena Petkova 
<\/strong>Assistant Professor
Department of Mathematics 
<\/i>Faculty of Natural Sciences and Education
Ruse University \u201eA. Kanchev\u201c<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a> \u0421\u0422\u0420\u0410\u0422\u0415\u0413\u0418\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415 \u0412 \u0421\u0420\u0415\u0414\u0410 \u0417\u0410 \u0415\u041b\u0415\u041a\u0422\u0420\u041e\u041d\u041d\u041e \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415<\/p>\n

<\/strong>\u0412\u0435\u043d\u0446\u0438\u0441\u043b\u0430\u0432 \u0414\u0436\u0430\u043c\u0431\u0430\u0437\u043e\u0432<\/p>\n

<\/strong>Abstract. <\/strong>\u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0438 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f, \u0441\u0432\u044a\u0440\u0437\u0430\u043d\u0438 \u0441 \u043f\u0440\u043e\u0432\u0435\u0436\u0434\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435. \u0418\u0437\u0432\u044a\u0440\u0448\u0435\u043d\u0430 \u0435 \u043a\u043b\u0430\u0441\u0438\u0444\u0438\u043a\u0430\u0446\u0438\u044f \u043d\u0430 \u0443\u0447\u0435\u0431\u043d\u0438\u0442\u0435 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u0438 \u043d\u0430 \u0431\u0430\u0437\u0430\u0442\u0430 \u043d\u0430 \u0442\u0435\u0445\u043d\u0438\u044f \u043c\u0435\u0434\u0438\u0435\u043d \u0444\u043e\u0440\u043c\u0430\u0442. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0438 \u0441\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0442\u0435 \u0443\u0447\u0435\u0431\u043d\u0438 \u0434\u0435\u0439\u043d\u043e\u0441\u0442\u0438, \u043f\u0440\u0438\u043b\u043e\u0436\u0438\u043c\u0438 \u0432 \u0435\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0430 \u0441\u0440\u0435\u0434\u0430. \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0441\u0430 \u043d\u044f\u043a\u043e\u0438 \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u0447\u043d\u0438 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u0430\u0441\u043f\u0435\u043a\u0442\u0438.

Keywords<\/i>:electronic education, learning materials, learning activities, classification, methodology

TEACHING STRATEGIES IN E-LEARNING ENVIRONMENT<\/p>\n

<\/strong>Abstract. <\/strong>The paper considers basic matters connected to e-learning performance. A classification of learning materials is carried out on the base of their mass media format. Basic learning activities are presented concerning applications in electronic media. Some specific methodological aspects are considered, too.  

Vencislav Dzambazov
<\/strong>Associated Professor, PhD
\u201eInformatics\u201c Department
New Bulgarian University<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a>\u041c\u0410\u0428\u0418\u041d\u041d\u0410 \u0410\u0420\u0418\u0422\u041c\u0415\u0422\u0418\u041a\u0410 \u0412 \u0427\u0410\u0421\u041e\u0412\u0415\u0422\u0415 \u041f\u041e \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0422\u0418\u041a\u0410<\/p>\n

<\/strong>Plamen Penev<\/p>\n

<\/strong>Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u043f\u0440\u0430\u0432\u0438 \u043e\u043f\u0438\u0442 \u0437\u0430 \u0438\u0437\u043b\u0438\u0437\u0430\u043d\u0435 \u0438\u0437\u0432\u044a\u043d \u0448\u0430\u0431\u043b\u043e\u043d\u0430 \u043d\u0430 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043f\u043e\u0437\u0438\u0446\u0438\u043e\u043d\u043d\u0438 \u0431\u0440\u043e\u0439\u043d\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0432 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0438\u044f \u043a\u0443\u0440\u0441 \u043f\u043e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430. \u0427\u0440\u0435\u0437 \u043f\u0440\u0430\u0432\u0430 \u0438 \u043e\u0431\u0440\u0430\u0442\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f\u0442\u0430 \u0441 \u0434\u0432\u043e\u0438\u0447\u043d\u0438 \u0447\u0438\u0441\u043b\u0430 \u0441\u0435 \u043f\u0440\u0435\u043d\u0430\u0441\u044f\u0442 \u0432 \u043c\u0430\u0448\u0438\u043d\u043d\u0430\u0442\u0430 \u043f\u0430\u043c\u0435\u0442. \u041f\u0440\u0438 \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0444\u043e\u0440\u043c\u0438\u0442\u0435 \u043d\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044f\u043d\u0435 \u0441\u0435 \u043e\u0431\u0440\u044a\u0449\u0430 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043e\u0441\u043e\u0431\u0435\u043d\u043e\u0441\u0442\u0438, \u0438\u0437\u044f\u0441\u043d\u044f\u0432\u0430\u0449\u0438 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u201e\u0442\u0438\u043f \u0434\u0430\u043d\u043d\u0438\u201c. \u0412\u044a\u0432\u0435\u0436\u0434\u0430\u0442 \u0441\u0435 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0438 \u043c\u0430\u0448\u0438\u043d\u043d\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043a\u043e\u0438\u0442\u043e \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0437\u0438\u0440\u0430\u0442 \u0440\u0430\u0431\u043e\u0442\u0430\u0442\u0430 \u043d\u0430 \u0438\u0437\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430.

Keywords<\/i>: binary numeral system, integer type data, coding of numbers, forward and inverse problem, machine register

MACHINE ARITHMETIC IN INFORMATICS CLASSES<\/p>\n

<\/strong>Abstract.<\/strong> An attempt is done in the paper to break out of the teaching pattern concerning positional numeral systems in the Informatics curriculum. Operations with binary numbers are transferred to the machine memory by forward and inverse problems. Some peculiarities clarifying the \u201cdata type\u201d notion are emphasized in the observation process of presenting forms. Elementary machine operations are introduced, thus characterizing the computing system performance.

Plamen Penev
<\/strong>Teacher
\u201ePanayot Volov\u201c school
Shumen, Bulgaria<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

 <\/a> \u041a\u0420\u0418\u0422\u0415\u0420\u0418\u0418 \u0417\u0410 \u041e\u0426\u0415\u041d\u041a\u0410 \u041d\u0410 \u041f\u0420\u041e\u0415\u041a\u0422\u0418 \u041f\u041e \u0418\u041d\u0424\u041e\u0420\u041c\u0410\u0426\u0418\u041e\u041d\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418 \u0412 \u041f\u041b\u0410\u0422\u0424\u041e\u0420\u041c\u0410\u0422\u0410 E-TWINNING<\/p>\n

<\/strong>\u0414\u0430\u043d\u0438\u0435\u043b\u0430 \u0414\u0438\u043c\u0438\u0442\u0440\u043e\u0432\u0430<\/p>\n

<\/strong>Abstract. <\/strong>\u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u0443\u043a\u0430\u0437\u0430\u043d\u0438\u044f \u0437\u0430 \u0441\u0442\u0430\u0440\u0442\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043f\u0440\u043e\u0435\u043a\u0442 \u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e\u043c \u043f\u043b\u0430\u0442\u0444\u043e\u0440\u043c\u0430\u0442\u0430 e-Twinning \u0438 \u0441\u0435 \u0440\u0430\u0437\u044f\u0441\u043d\u044f\u0432\u0430\u0442 \u043a\u0440\u0438\u0442\u0435\u0440\u0438\u0438\u0442\u0435 \u0437\u0430 \u043e\u0446\u0435\u043d\u043a\u0430 \u043d\u0430 \u043f\u0440\u043e\u0435\u043a\u0442\u0438, \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0435\u043d\u0438 \u0447\u0440\u0435\u0437 \u043d\u0435\u044f. \u0418\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u0442 \u0441\u0435 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u043e\u0442 \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442. \u0415\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430\u0442\u0430 \u0433\u0440\u0443\u043f\u0430 \u0448\u0435\u0441\u0442\u043e\u043a\u043b\u0430\u0441\u043d\u0438\u0446\u0438 \u043f\u043e\u043f\u0430\u0434\u0430 \u0432\u044a\u0432 \u0432\u044a\u0437\u0440\u0430\u0441\u0442\u043e\u0432\u0430\u0442\u0430 \u0433\u0440\u0430\u043d\u0438\u0446\u0430 \u043e\u0442 11 \u0434\u043e 14 \u0433\u043e\u0434\u0438\u043d\u0438. \u0414\u043e\u043a\u0430\u0437\u0432\u0430 \u0441\u0435, \u0447\u0435 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u0447\u0440\u0435\u0437 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430 \u043d\u0430 \u043f\u0440\u043e\u0435\u043a\u0442\u0438 \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 \u0432 \u043f\u0440\u043e\u0433\u0438\u043c\u043d\u0430\u0437\u0438\u0430\u043b\u043d\u0438\u044f \u0435\u0442\u0430\u043f \u0437\u0430\u0442\u0432\u044a\u0440\u0436\u0434\u0430\u0432\u0430, \u0440\u0430\u0437\u0432\u0438\u0432\u0430 \u0438 \u043d\u0430\u0434\u0433\u0440\u0430\u0436\u0434\u0430 \u043f\u0440\u0438\u0434\u043e\u0431\u0438\u0442\u0438\u0442\u0435 \u0437\u043d\u0430\u043d\u0438\u044f \u0438 \u0443\u043c\u0435\u043d\u0438\u044f \u0432 \u0447\u0430\u0441\u043e\u0432\u0435\u0442\u0435 \u043e\u0442 \u0437\u0430\u0434\u044a\u043b\u0436\u0438\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430. \u0426\u0435\u043b\u0442\u0430 \u0435 \u043f\u043e\u0432\u0438\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u043f\u0438\u0442\u0430 \u0437\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0432 \u0435\u043a\u0438\u043f \u0438 \u043f\u043e\u0432\u0438\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043f\u043e\u0437\u043d\u0430\u0432\u0430\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u0430\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438\u0442\u0435.

Keywords:<\/i>information technology, eTwinning, teamwork, cognitive activity

CRITERIA FOR EVALUATION OF INFORMATION TECHNOLOGY PROJECTS IN THE E-TWINNING PLATFORM<\/p>\n

<\/strong>Abstract. <\/strong>M<\/span>ethodological instructions are considered in the paper for launching a project by means of the platform eTwinning, and some criteria are explained for the evaluation of projects elaborated through it. The results of a conducted pedagogical experiment are used. The experimental group of 6-th graders falls in the age limit of 11 to 14-year olds. It is proved that education through elaborating information technology projects in the junior high school consolidates, develops and upgrades the acquired knowledge and skills during the classes of mandatory training. The objective is to gain experience through team work and to increase the cognitive activity of the students.

Daniela Dimitrova
<\/strong>PhD student 
Department \u201eComputer Technologies\u201c
Plovdiv University<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

","protected":false},"excerpt":{"rendered":"

 \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS Five New Proofs of One Trigonometric Inequality in the Triangle \u041f\u0435\u0442 \u043d\u043e\u0432\u0438 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430 \u043d\u0430 \u0435\u0434\u043d\u043e \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0432 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 \/\u0160efket Arslanagi\u0107, Alija Muminagi\u0107 \/ \u0428\u0435\u0444\u043a\u0435\u0442 \u0410\u0440\u0441\u043b\u0430\u043d\u0430\u0433\u0438\u0447, \u0410\u043b\u0438\u044f \u041c\u0443\u043c\u0438\u043d\u0430\u0433\u0438\u0447 – 505   \u0415\u0434\u043d\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0437\u0430 \u0442\u0440\u0430\u043f\u0435\u0446 A Generalization of an Inequality for Trapezoid \/\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Veselin Nenkov – 509   \u041f\u0440\u043e\u0435\u043a\u0442\u0438\u0432\u043d\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u043d\u0438 \u043a\u0440\u0438\u0432\u0438, […]<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[]},"categories":[2882],"tags":[],"yoast_head":"\n"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430", \u043a\u043d\u0438\u0436\u043a\u0430 6, \u0433\u043e\u0434\u0438\u043d\u0430 LVI, 2013 - \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:\/\/mathinfo.azbuki.bg\/matematics\/matharticles\/mathinfo062013\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\""\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430", \u043a\u043d\u0438\u0436\u043a\u0430 6, \u0433\u043e\u0434\u0438\u043d\u0430 LVI, 2013 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\" \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS Five New Proofs of One Trigonometric Inequality in the Triangle \u041f\u0435\u0442 \u043d\u043e\u0432\u0438 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u0430 \u043d\u0430 \u0435\u0434\u043d\u043e \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0432 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 \/\u0160efket Arslanagi\u0107, Alija Muminagi\u0107 \/ \u0428\u0435\u0444\u043a\u0435\u0442 \u0410\u0440\u0441\u043b\u0430\u043d\u0430\u0433\u0438\u0447, \u0410\u043b\u0438\u044f \u041c\u0443\u043c\u0438\u043d\u0430\u0433\u0438\u0447 – 505   \u0415\u0434\u043d\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0437\u0430 \u0442\u0440\u0430\u043f\u0435\u0446 A Generalization of an Inequality for Trapezoid \/\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Veselin Nenkov – 509   \u041f\u0440\u043e\u0435\u043a\u0442\u0438\u0432\u043d\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0438\u0447\u043d\u0438 \u043a\u0440\u0438\u0432\u0438, […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathinfo.azbuki.bg\/matematics\/matharticles\/mathinfo062013\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Azbuki55\/\" \/>\n<meta property=\"article:published_time\" content=\"2013-11-03T11:16:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-06-24T14:33:15+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathinfo.azbuki.bg\/matematics\/matharticles\/mathinfo062013\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathinfo.azbuki.bg\/matematics\/matharticles\/mathinfo062013\/\"},\"author\":{\"name\":\"\",\"@id\":\"\"},\"headline\":\"„\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430“, \u043a\u043d\u0438\u0436\u043a\u0430 6, \u0433\u043e\u0434\u0438\u043d\u0430 LVI, 2013\",\"datePublished\":\"2013-11-03T11:16:00+00:00\",\"dateModified\":\"2019-06-24T14:33:15+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathinfo.azbuki.bg\/matematics\/matharticles\/mathinfo062013\/\"},\"wordCount\":1918,\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"articleSection\":[\"\u0421\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u043d\u0430 \u0441\u043f. \\\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\\\"\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathinfo.azbuki.bg\/matematics\/matharticles\/mathinfo062013\/\",\"url\":\"https:\/\/mathinfo.azbuki.bg\/matematics\/matharticles\/mathinfo062013\/\",\"name\":\"\\\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\\\", \u043a\u043d\u0438\u0436\u043a\u0430 6, \u0433\u043e\u0434\u0438\u043d\u0430 LVI, 2013 - 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