{"id":38233,"date":"2013-04-27T21:59:29","date_gmt":"2013-04-27T18:59:29","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/"},"modified":"2019-06-24T17:33:15","modified_gmt":"2019-06-24T14:33:15","slug":"matematika-i-informatika-knizhka-1-godina-lvi-2014","status":"publish","type":"post","link":"https:\/\/science.azbuki.bg\/en\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/","title":{"rendered":"Mathematics and Informatics, Number 2\/2013, Volume 56"},"content":{"rendered":"

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

Topic of the issue: computer technologies in mathematics education<\/em>
The development of IT allows for conversion<\/em>
of Mathematics into Experimental Science.This issue is dedicated to<\/em>
the computer-based learning approach.<\/em><\/p>\n

\u0415\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u0443\u0447\u0438\u043b\u0438\u0449\u0435 <\/a>
[Experimental Mathematics at School] \/<\/a>
\u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev \/ \u0411. \u041b\u0430\u0437\u0430\u0440\u043e\u0432 \/ B. Lazarov<\/em> – \u0441\u0442\u0440. 104<\/p>\n

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\u201e\u0412\u044b\u0445\u043e\u0434 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e\u201c \u0441 \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0440\u0435\u0434\u043e\u0439 <\/a>
[\u201eExit Into The Space\u201c By Interactive geometric Environment] \/<\/a>
\u041c. \u0428\u0430\u0431\u0430\u043d\u043e\u0432\u0430 \/ M. Shabanova \/ \u0421. \u041a\u043e\u0442\u043e\u0432\u0430 \/ S. Kotova<\/em> - p. 113<\/p>\n

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\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0441 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440 <\/a>
[Mathematics With Computer] \/ <\/a>
\u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev \/ \u0414. \u0414\u0435\u043a\u043e\u0432 \/ D. Dekov<\/em> – \u0441\u0442\u0440. 123<\/p>\n

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\u0418\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u043e \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043e\u043f\u0438\u0441\u0430\u043d\u0438 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438 \u0432 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u043d\u0430 \u0441\u0440\u0435\u0434\u0430 <\/a>
[Interactive Study Of Circumscribed Quadrilaterals In Dynamic Environment] <\/a>\/
\u0411. \u0426\u0430\u0440\u0435\u0432\u0430 \/ B. Tsareva \/ \u0420. \u0422\u043e\u0434\u043e\u0440\u043e\u0432\u0430 \/ R. Todorova<\/em> - p. 142<\/p>\n

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\u0415\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u043d \u0410\u0440\u0431\u0435\u043b\u043e\u0441 <\/a>
[Elliptic Arbelos] \/ <\/a>
\u041f. \u041b\u0430\u0437\u0430\u0440\u043e\u0432\u0430 \/ P. Lazarova<\/em> – \u0441\u0442\u0440. 159<\/p>\n

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\u0422\u0440\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438 \u043e\u0442 \u0432\u0438\u0441\u043e\u0447\u0438\u043d\u0438\u0442\u0435 \u043c\u0443 <\/a>
[Three Properties Of The Triangle Generated By Its Altitudes] \/ <\/a>
\u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev \/ \u0412. \u041d\u0435\u043d\u043a\u043e\u0432 \/ V. Nenkov<\/em> – \u0441\u0442\u0440. 176<\/p>\n

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\u041c\u0430\u0440\u043a\u0435\u0442\u0438\u043d\u0433\u043e\u0432\u0438 \u043f\u0440\u043e\u0443\u0447\u0432\u0430\u043d\u0438\u044f \u0441 \u0443\u0447\u0438\u043b\u0438\u0449\u043d\u0438 \u0437\u043d\u0430\u043d\u0438\u044f <\/a>
[Marketing Research With School Knoledge] \/ <\/a>
\u0412. \u0411\u0438\u0437\u043e\u0432\u0430 \u2013 \u041b\u0430\u043b\u0435\u0432\u0430 \/ V. Bizova \u2013 Laleva<\/em> – \u0441\u0442\u0440. 184<\/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<\/strong>
\u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f –<\/strong> \u0441\u0442\u0440. 192
\u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u043a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438\u0442\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u0431\u0440\u043e\u0439 3, 2012 – <\/strong>\u0441\u0442\u0440. 193<\/p>\n

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\u0412 \u043d\u043e\u0432\u0438\u0442\u0435 \u0431\u0440\u043e\u0435\u0432\u0435 \u043d\u0430 \u0441\u043f\u0438\u0441\u0430\u043d\u0438\u044f\u0442\u0430 \u043d\u0430 \u0438\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e \u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c \u0447\u0435\u0442\u0435\u0442\u0435 \/ <\/strong>
Read in The Latest Issues of \u201eAz Buki\u201c Journals<\/strong> – \u0441\u0442\u0440. 195<\/p>\n

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\u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415 \/ GUIDE FOR AUTHORS<\/strong> – \u0441\u0442\u0440. 197<\/p>\n

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 <\/p>\n

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 <\/a>\u0415\u041a\u0421\u041f\u0415\u0420\u0418\u041c\u0415\u041d\u0422\u0410\u041b\u041d\u0410\u0422\u0410 \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 <\/strong>\u0412 \u0423\u0427\u0418\u041b\u0418\u0429\u0415<\/strong><\/p>\n

\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0411\u043e\u0440\u0438\u0441\u043b\u0430\u0432 \u041b\u0430\u0437\u0430\u0440\u043e\u0432<\/strong><\/p>\n

Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d \u043e\u0431\u0437\u043e\u0440 \u043d\u0430 \u0438\u0434\u0435\u0438\u0442\u0435 \u0437\u0430 \u043c\u044f\u0441\u0442\u043e\u0442\u043e \u0438 \u0440\u043e\u043b\u044f\u0442\u0430 \u043d\u0430 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430.<\/p>\n

Keywords:<\/em> Socratic style, experimental approach, synthetic competence, individual educational trajectory.<\/p>\n

 <\/p>\n

EXPERIMENTAL MATHEMATICS AT SCHOOL<\/strong><\/p>\n

Abstract.<\/strong> The paper presents a review of ideas concerning the place and the role of experiment in Mathematics teaching.<\/p>\n

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

Borislav Lazarov<\/strong>
Associated Professor, Doctor in Pedagogy<\/em>
Institute of Mathematics and Informatics \u2013 BAS<\/em>
Sofia, Bulgaria<\/em><\/p>\n

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

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 <\/a>\u201e\u0412\u044b\u0445\u043e\u0434 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e\u201c \u0441 \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u043e\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0440\u0435\u0434\u043e\u0439<\/strong><\/p>\n


<\/strong>\u041c\u0430\u0440\u0438\u044f \u0428\u0430\u0431\u0430\u043d\u043e\u0432\u0430, \u0421\u0432\u0435\u0442\u043b\u0430\u043d\u0430 \u041a\u043e\u0442\u043e\u0432\u0430<\/strong><\/p>\n

Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u044b \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u0435\u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0435\u0439 \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u043d\u044b\u0445 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u0440\u0435\u0434 \u0432 \u0441\u043e\u0437\u0434\u0430\u043d\u0438\u0438 \u0432\u0438\u0440\u0442\u0443\u0430\u043b\u044c\u043d\u044b\u0445 \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432. \u0410\u0432\u0442\u043e\u0440\u044b \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u044e\u0442, \u043a\u0430\u043a \u043f\u0440\u0438\u0435\u043c\u044b \u201e\u0432\u044b\u0445\u043e\u0434 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e\u201c \u0438 \u201e\u0443\u0445\u043e\u0434 \u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c\u201c \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u044b \u043f\u0440\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438 \u0434\u043b\u044f \u043f\u0440\u0435\u043e\u0434\u043e\u043b\u0435\u043d\u0438\u044f \u043d\u0435\u0434\u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u044f \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0433\u043e \u0432\u043e\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0438 \u043c\u044b\u0448\u043b\u0435\u043d\u0438\u044f \u0443\u0447\u0430\u0449\u0438\u0445\u0441\u044f.<\/p>\n

Keywords:<\/em> Geometry education, interactive geometric environment, virtual model of instrumental type<\/p>\n

 <\/p>\n

\u201eEXIT INTO THE SPACE\u201c <\/strong>BY INTERACTIVE GEOMETRIC ENVIRONMENT<\/strong><\/p>\n

Abstract.<\/strong> The paper presents a methodological approach to the applicable possibilities of interactive geometric environment for the creation of virtual instrumental models of geometric objects. The authors show how \u201eexit into the space\u201c and \u201egoing to the plane\u201c could be used in Geometry education to overcome defects in the development of spatial imagination and thinking of students.<\/p>\n

Maria Shabanova<\/strong>
Professor, DSc in Pedagogy<\/em>
Institute of Mathematics and Computer Science<\/em>
Arkhangelsk, Russia<\/em><\/p>\n

Svetlana Kotova<\/strong>
Associated Professor, PhD in Pedagogy<\/em>
Institute of Mathematics and Computer Science<\/em>
Arkhangelsk, Russia<\/em><\/p>\n

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

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 <\/p>\n

 <\/a>\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u0421 \u041a\u041e\u041c\u041f\u042e\u0422\u042a\u0420<\/strong><\/p>\n

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

Abstract.<\/strong> \u0410\u0432\u0442\u043e\u0440\u0438\u0442\u0435 \u0434\u0438\u0441\u043a\u0443\u0442\u0438\u0440\u0430\u0442 \u0432\u044a\u043f\u0440\u043e\u0441\u0430 \u0437\u0430 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0435\u0437\u0438\u043a \u0437\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0438\u0440\u0430\u043d\u0435 \u0432 \u0441\u0440\u0435\u0434\u043d\u043e\u0442\u043e \u0443\u0447\u0438\u043b\u0438\u0449\u0435 \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u0442 \u0443\u0447\u0435\u0431\u043d\u0438\u044f \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0430 \u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430.<\/p>\n

Keywords:<\/em> problem solving, computer, programming language, browser, JavaScript, PHP, the money-exchanging problem<\/p>\n

 <\/p>\n

MATHEMATICS WITH COMPUTER<\/strong><\/p>\n

Abstract.<\/strong> The authors discuss the use of programming language to solve curriculum mathematical problems in high school. A programme is proposed for the solution of a particular problem.<\/p>\n

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

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

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

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 <\/p>\n

 <\/a>\u0418\u041d\u0424\u041e\u0420 \u041c\u0410\u0426\u0418\u041e\u041d\u041d\u0418\u0422\u0415 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418 <\/strong>\u0412 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410:<\/strong>
\u0421\u0420\u0415\u0414\u0421\u0422\u0412\u041e \u0417\u0410 \u0418\u041b\u0418 \u0411\u0410\u0420\u0418\u0415\u0420\u0410 \u041f\u0420\u0415\u0414 \u0424\u041e\u0420 \u041c\u0418\u0420\u0410\u041d\u0415\u0422\u041e <\/strong>\u041d\u0410 \u0410\u0411\u0421\u0422\u0420\u0410\u041a\u0422\u041d\u041e \u041c\u0418\u0421\u041b\u0415\u041d\u0415<\/strong><\/p>\n

\u0422\u0430\u043d\u044f \u0422\u043e\u043d\u043e\u0432\u0430, \u041d\u0438\u043a\u043e\u043b\u0438\u043d\u0430 \u041d\u0438\u043a\u043e\u043b\u043e\u0432\u0430<\/strong><\/p>\n

Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u043f\u0440\u0430\u0432\u0438 \u043a\u0440\u0430\u0442\u044a\u043a \u043f\u0440\u0435\u0433\u043b\u0435\u0434 \u043d\u0430 \u0430\u043a\u0442\u0443\u0430\u043b\u043d\u043e\u0442\u043e \u0441\u044a\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043d\u0430 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438\u0442\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u0438\u0437\u043e\u0431\u0449\u043e \u0438 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442. \u0421\u043f\u0435\u0446\u0438\u0430\u043b\u043d\u043e \u043c\u044f\u0441\u0442\u043e \u0435 \u043e\u0442\u0434\u0435\u043b\u0435\u043d\u043e \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0430\u0442\u0430 \u0446\u0435\u043b \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0442\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u2013 \u0434\u0430 \u0440\u0430\u0437\u0432\u0438\u0435 \u0430\u0431\u0441\u0442\u0440\u0430\u043a\u0442\u043d\u043e\u0442\u043e \u043c\u0438\u0441\u043b\u0435\u043d\u0435 \u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u043d\u043e\u0441\u0442\u0442\u0430 \u0434\u0430 \u0441\u0435 \u0438\u0437\u0432\u044a\u0440\u0448\u0432\u0430\u0442 \u0434\u0435\u0434\u0443\u043a\u0442\u0438\u0432\u043d\u0438 \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u044f. \u0410\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0430\u043d\u0430 \u0435 \u0440\u043e\u043b\u044f\u0442\u0430 \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438\u0442\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438
\u0437\u0430 \u043f\u043e\u0441\u0442\u0438\u0433\u0430\u043d\u0435 \u043d\u0430 \u0442\u0430\u0437\u0438 \u0446\u0435\u043b \u0432 \u043e\u0431\u0449 \u0438 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u0435\u043d \u043f\u043b\u0430\u043d. \u041f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u0438 \u0441\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u043e\u0442 \u0440\u0435\u0430\u043b\u043d\u0430\u0442\u0430 \u0443\u0447\u0435\u0431\u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0430. \u0412 \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435 \u0441\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0430\u043d\u0438 \u043f\u0440\u0435\u043f\u043e\u0440\u044a\u043a\u0438 \u043d\u0430 \u0431\u0430\u0437\u0430\u0442\u0430 \u043d\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u0435\u043d\u0438\u0442\u0435 \u0438\u0437\u0432\u043e\u0434\u0438.<\/p>\n

Keywords:<\/em> mathematics education, integration of IT in education \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0430\u043d\u0435, abstract thinking, school practice<\/p>\n

 <\/p>\n

INFORMATION TECHNOLOGIES IN MATHEMATICS EDUCATION:
TOOL FOR OR BARR IER AGAINST <\/span><\/strong>FORMING ABSTRACT THIN KING<\/strong><\/span><\/p>\n

Abstract.<\/strong> In the article is reviewed the current state of using ICT in education in general and specifically in the field of mathematics education. Special attention is devoted to the fundamental goal of mathematics education \u2013 to develop abstract thinking and the ability to conduct deductive reasoning. The role of ICT for achieving this goal in analyzed both broadly and in specific aspect. Examples of the actual school practice are shown. Finally, some recommendations are formulated based on the reached conclusions.<\/p>\n

Tanya Tonova<\/strong>
Faculty of Mathematics and Informatics<\/em>
Sofia University \u201eSt. Kl. Ohridski\u201d<\/em>
Sofia, Bulagria<\/em><\/p>\n

Nikolina Nikolova<\/strong>
Faculty of Mathematics and Informatics<\/em>
Sofia University \u201eSt. Kl. Ohridski\u201d<\/em>
Sofia, Bulagria<\/em><\/p>\n

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

\n

 <\/p>\n

 <\/a>\u0418\u041d\u0422\u0415\u0420\u0410\u041a\u0422\u0418\u0412\u041d\u041e \u0418\u0417\u0423\u0427\u0410\u0412\u0410\u041d\u0415 <\/strong>\u041d\u0410 \u041e\u041f\u0418\u0421\u0410\u041d\u0418 \u0427\u0415\u0422\u0418\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u0426\u0418 <\/strong>\u0412 \u0414\u0418\u041d\u0410\u041c\u0418\u0427\u041d\u0410 \u0421\u0420\u0415\u0414\u0410<\/strong><\/p>\n

\u0411\u0438\u0441\u0442\u0440\u0430 \u0426\u0430\u0440\u0435\u0432\u0430, \u0420\u0430\u0434\u043a\u0430 \u0422\u043e\u0434\u043e\u0440\u043e\u0432\u0430<\/strong><\/p>\n

Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d\u0430 \u043d\u0430 \u043f\u043e\u0434\u0445\u043e\u0434\u0430 \u043d\u0430 \u043f\u0440\u043e\u0443\u0447\u0432\u0430\u043d\u0435\u0442\u043e \u0441 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440, \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d \u043a\u044a\u043c \u0442\u0435\u043c\u0430\u0442\u0430 \u201e\u043e\u043f\u0438\u0441\u0430\u043d\u0438 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u0446\u0438\u201c.<\/p>\n

K\u0435\u0443words:<\/em> learning, circumscribed quadrilateral, computer, dynamical environment.<\/p>\n

 <\/p>\n

INTERACTIVE STUDY OF CIRCUMSCRIBED QUADRILATERALS <\/strong>IN DYNAMIC ENVIRONMENT<\/strong><\/p>\n

Absract.<\/strong> The paper is dedicated to the computer based inquiry approach to the topic of circumscribed quadrilaterals.<\/p>\n

Bistra Tsareva<\/strong>
Associated Professor, PhD<\/em>
Plovdiv University \u201eP. Hilendarski\u201c<\/em>
Plovdiv, Bulgaria<\/em><\/p>\n

Radka Todorova<\/strong>
Mathematics teacher<\/em>
High School \u201eH. Prodanov\u201c<\/em>
Karlovo, Bulgaria<\/em><\/p>\n

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

\n

 <\/p>\n

 <\/a>\u0415\u041b\u0418\u041f\u0422\u0418\u0427\u0415\u041d \u0410\u0420\u0411\u0415\u041b\u041e\u0421<\/strong><\/p>\n

\u041f\u0440\u043e\u043b\u0435\u0442 \u041b\u0430\u0437\u0430\u0440\u043e\u0432\u0430<\/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 \u0444\u0438\u0433\u0443\u0440\u0430\u0442\u0430 \u0435\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u043d \u0430\u0440\u0431\u0435\u043b\u043e\u0441 \u2013 \u0435\u043b\u0438\u043f\u0441\u0430 \u0438 \u0434\u0432\u0435 \u0434\u043e\u043f\u0438\u0440\u0430\u0449\u0438 \u044f \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438 \u0441 \u0446\u0435\u043d\u0442\u0440\u043e\u0432\u0435 \u0432\u044a\u0432 \u0444\u043e\u043a\u0443\u0441\u0438\u0442\u0435 \u0439. \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0441\u0430 \u0442\u0440\u0438 \u0442\u0438\u043f\u0430 \u0435\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u043d \u0430\u0440\u0431\u0435\u043b\u043e\u0441 \u2013 \u0442\u0430\u043d\u0433\u0435\u043d\u0446\u0438\u0430\u043b\u0435\u043d, \u043f\u0440\u0435\u0441\u0435\u043a\u0430\u0442\u0435\u043b\u0435\u043d \u0438 \u043d\u0435\u043f\u0440\u0435\u0441\u0435\u043a\u0430\u0442\u0435\u043b\u0435\u043d. \u0414\u043e\u043a\u0430\u0437\u0430\u043d\u0438 \u0441\u0430 \u043d\u044f\u043a\u043e\u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u0438 \u0440\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438, \u0434\u0430\u0434\u0435\u043d\u0438 \u0441\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0438 \u0437\u0430 \u043a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438 \u0442\u0438\u043f \u0421\u0430\u043d\u0433\u0430\u043a\u0443. \u0418\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0430 \u0435 \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u043a\u0446\u0438\u044f \u043e\u0442 \u0434\u043e\u043f\u0438\u0440\u0430\u0442\u0435\u043b\u043d\u0438 \u0438 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0438 \u043a\u044a\u043c \u0442\u044f\u0445 \u0438 \u0432\u0440\u044a\u0437\u043a\u0430\u0442\u0430 \u0441 \u0442\u0438\u043f\u043e\u0432\u0435\u0442\u0435
\u0435\u043b\u0438\u043f\u0442\u0438\u0447\u0435\u043d \u0430\u0440\u0431\u0435\u043b\u043e\u0441. \u0412\u044a\u0432\u0435\u0434\u0435\u043d\u043e \u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u0442\u043e \u0410\u0440\u0445\u0438\u043c\u0435\u0434\u043e\u0432\u0438 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438 \u0432 \u0435\u043b\u0438\u043f\u0442\u0438\u0447\u043d\u0438\u044f \u0430\u0440\u0431\u0435\u043b\u043e\u0441 \u0438 \u0435 \u043e\u043f\u0438\u0441\u0430\u043d \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u044a\u043c \u0437\u0430 \u043f\u043e\u0441\u0442\u0440\u043e\u044f\u0432\u0430\u043d\u0435\u0442\u043e \u0438\u043c \u0441\u044a\u0441 \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0437\u0430 \u0434\u0438\u043d\u0430\u043c\u0438\u0447\u043d\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f. \u0424\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0430\u043d\u0438 \u0441\u0430 \u043e\u0442\u0432\u043e\u0440\u0435\u043d\u0438 \u0432\u044a\u043f\u0440\u043e\u0441\u0438.<\/p>\n

Keywords:<\/em> elliptic arbelos, Sangaku, Archimedes\u2019 circles<\/p>\n

 <\/p>\n

ELLIPTIC ARBELOS<\/strong><\/p>\n

Abstract.<\/strong> The article considers an extension of the concept of the Archimedes arbelos. The elliptic arbelos consists of two circles (generating circles) which define an ellipse with foci in their centers. Three types of elliptic arbeloses are considered: tangential, intersecting and non-intersecting. Basic properties of the figure are established and formed as theorems. A Sangaku-type problem in a Bulgarian mathematical journal
inspired the author to examine a specific configuration of tangents and perpendicular lines and their relation to the elliptic arbelos. The concept of generalized elliptic arbelos and Archimedes\u2019 circles in the generalized elliptic arbelos are introduced and an algorithm for their construction is designed. Some open questions are stated.<\/p>\n

Prolet Lazarova<\/strong>
Student<\/em>
Faculty of Physics, <\/em>
\u201eSt. Kliment Ochridski\u201c University,<\/em>
Sofia, Bulgaria<\/em><\/p>\n

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

\n

 <\/p>\n

 <\/a>\u0422\u0420\u0418 \u0421\u0412\u041e\u0419\u0421\u0422\u0412\u0410 \u041d\u0410 \u0422\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u041a\u0410, \u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u0418 \u041e\u0422 \u0412\u0418\u0421\u041e\u0427\u0418\u041d\u0418\u0422\u0415 \u041c\u0423<\/span><\/strong><\/p>\n

Sava Grozdev, Veselin Nenkov<\/strong><\/p>\n

Abstract.<\/strong> \u0421 \u043f\u043e\u043c\u043e\u0449\u0442\u0430 \u043d\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430\u0442\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u201eThe Geometer \u2019s Sketchpad \u201c \u0435 \u0438\u0437\u0441\u043b\u0435\u0434\u0432\u0430\u043d\u0430 \u0435\u0434\u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u043e\u0442 \u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430\u0442\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043f\u0440\u0435\u0437 2012 \u0433. \u041e\u0442\u043a\u0440\u0438\u0442\u0438 \u0438 \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u0438 \u0441\u0430 \u043d\u044f\u043a\u043e\u043b\u043a\u043e \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 \u0432\u044a\u0432 \u0432\u0440\u044a\u0437\u043a\u0430 \u0441 \u0432\u0438\u0441\u043e\u0447\u0438\u043d\u0438\u0442\u0435 \u043c\u0443.<\/p>\n

Keywords:<\/em> problem solving, triangle, altitude, The Geometer \u2019s Sketchpad<\/p>\n

 <\/p>\n

THREE PROPERTIES OF THE TRIANGLE GENERATED <\/strong>BY ITS ALTITUDES<\/strong><\/p>\n

Abstract.<\/strong> A problem from the International Mathematical Olympiad in 2012 is investigated by means of the computer software \u201eThe Geometer \u2019s Sketchpad \u201c. Some interesting properties of the triangle in connection with its altitudes are discovered and proved.<\/p>\n

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

Veselin Nenkov<\/strong>
Doctor in Pedagogy<\/em>
Technical College Lovech<\/em>
Lovech, Bulgaria<\/em><\/p>\n

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

\n

 <\/p>\n

 <\/a>\u041c\u0410\u0420\u041a\u0415\u0422\u0418\u041d\u0413\u041e\u0412\u0418 \u041f\u0420\u041e \u0423\u0427\u0412\u0410\u041d\u0418\u042f <\/strong>\u0421 \u0423\u0427\u0418\u041b\u0418\u0429\u041d\u0418 \u0417\u041d\u0410\u041d\u0418\u042f<\/strong><\/p>\n

\u0412\u0430\u043d\u044f \u0411\u0438\u0437\u043e\u0432\u0430 \u2013 \u041b\u0430\u043b\u0435\u0432\u0430<\/strong><\/p>\n

Abstract.<\/strong> \u041f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0442 \u0441\u0435 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0437\u043d\u0430\u043d\u0438\u044f \u043e\u0442 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u0430\u0442\u0430 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f, \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u0438 \u0432 \u0441\u0440\u0435\u0434\u043d\u043e\u0442\u043e \u0443\u0447\u0438\u043b\u0438\u0449\u0435 \u0438 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u0430\u0442\u0430 \u0441\u0440\u0435\u0434\u0430 GeoGebra, \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u0440\u0430\u0437\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u0430\u0437\u0430\u0440\u0430 \u043d\u0430 \u043f\u043e\u0442\u0440\u0435\u0431\u0438\u0442\u0435\u043b\u0438\u0442\u0435 \u043d\u0430 \u0441\u0442\u043e\u043a\u0438 \u0438 \u0443\u0441\u043b\u0443\u0433\u0438.<\/p>\n

Keywords:<\/em> dynamic software, GeoGebra, practical tasks<\/p>\n

 <\/p>\n

MARKETING RESEARCH WITH SCHOOL KNOWLEDGE<\/strong><\/p>\n

Abstract.<\/strong> There are some applications of mathematical knowledge of elementary geometry, which is taught at the secondary school level, and the programming environment GeoGebra, for the solution of practical problems in the market distribution of consumers of goods and services.<\/p>\n

Vania Bizova\u2013Laleva<\/strong>
National School of Commerce, Plovdiv<\/em>
Plovdiv, Bulgaria<\/em><\/p>\n

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

\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>","protected":false},"excerpt":{"rendered":"

 \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \/ CONTENTS \u0422\u0435\u043c\u0430 \u043d\u0430 \u0431\u0440\u043e\u044f: \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438\u0442\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435\u0442\u043e \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438\u0442\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0434\u0430\u0432\u0430\u0442 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442 \u0437\u0430 \u043f\u0440\u0435\u0432\u0440\u044a\u0449\u0430\u043d\u0435\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0442\u0430 \u0432 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430 \u043d\u0430\u0443\u043a\u0430. \u041d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u044f\u0442 \u0431\u0440\u043e\u0439 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d \u043d\u0430\u043f\u0440\u043e\u0443\u0447\u0432\u0430\u0442\u0435\u043b\u043d\u0438\u044f \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u0443\u0447\u0435\u043d\u0435\u0442\u043e, \u043a\u043e\u0439\u0442\u043e \u0441\u0435 \u043e\u0441\u043d\u043e\u0432\u0430\u0432\u0430 \u043d\u0430 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440. \u0415\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u0443\u0447\u0438\u043b\u0438\u0449\u0435 [Experimental Mathematics at School] \/\u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev \/ \u0411. \u041b\u0430\u0437\u0430\u0440\u043e\u0432 \/ […]<\/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 2, \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:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/\" \/>\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 2, \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 \u0422\u0435\u043c\u0430 \u043d\u0430 \u0431\u0440\u043e\u044f: \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0438\u0442\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0420\u0430\u0437\u0432\u0438\u0442\u0438\u0435\u0442\u043e \u043d\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u0438\u0442\u0435 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0438 \u0434\u0430\u0432\u0430\u0442 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442 \u0437\u0430 \u043f\u0440\u0435\u0432\u0440\u044a\u0449\u0430\u043d\u0435\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u0442\u0430 \u0432 \u0435\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430 \u043d\u0430\u0443\u043a\u0430. \u041d\u0430\u0441\u0442\u043e\u044f\u0449\u0438\u044f\u0442 \u0431\u0440\u043e\u0439 \u0435 \u043f\u043e\u0441\u0432\u0435\u0442\u0435\u043d \u043d\u0430\u043f\u0440\u043e\u0443\u0447\u0432\u0430\u0442\u0435\u043b\u043d\u0438\u044f \u043f\u043e\u0434\u0445\u043e\u0434 \u0432 \u0443\u0447\u0435\u043d\u0435\u0442\u043e, \u043a\u043e\u0439\u0442\u043e \u0441\u0435 \u043e\u0441\u043d\u043e\u0432\u0430\u0432\u0430 \u043d\u0430 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440. \u0415\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0432 \u0443\u0447\u0438\u043b\u0438\u0449\u0435 [Experimental Mathematics at School] \/\u0421. \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ S. Grozdev \/ \u0411. \u041b\u0430\u0437\u0430\u0440\u043e\u0432 \/ […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/\" \/>\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=\"2013-04-27T18:59:29+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:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/\"},\"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 2, \u0433\u043e\u0434\u0438\u043d\u0430 LVI, 2013\",\"datePublished\":\"2013-04-27T18:59:29+00:00\",\"dateModified\":\"2019-06-24T14:33:15+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/\"},\"wordCount\":1790,\"publisher\":{\"@id\":\"https:\/\/azbuki.bg\/#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:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/\",\"url\":\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/\",\"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 2, \u0433\u043e\u0434\u0438\u043d\u0430 LVI, 2013 - 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Grozdev \/ \u0411. \u041b\u0430\u0437\u0430\u0440\u043e\u0432 \/ […]","og_url":"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/","og_site_name":"\u0410\u0437-\u0431\u0443\u043a\u0438","article_publisher":"https:\/\/www.facebook.com\/Azbuki55\/","article_published_time":"2013-04-27T18:59:29+00:00","article_modified_time":"2019-06-24T14:33:15+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":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/#article","isPartOf":{"@id":"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/"},"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 2, \u0433\u043e\u0434\u0438\u043d\u0430 LVI, 2013","datePublished":"2013-04-27T18:59:29+00:00","dateModified":"2019-06-24T14:33:15+00:00","mainEntityOfPage":{"@id":"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/"},"wordCount":1790,"publisher":{"@id":"https:\/\/azbuki.bg\/#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:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/","url":"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles\/matematika-i-informatika-knizhka-1-godina-lvi-2014\/","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 2, \u0433\u043e\u0434\u0438\u043d\u0430 LVI, 2013 - 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