{"id":40387,"date":"2015-11-04T21:59:00","date_gmt":"2015-11-04T18:59:00","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles\/mathinfocontent062015\/"},"modified":"2019-06-24T17:33:14","modified_gmt":"2019-06-24T14:33:14","slug":"mathinfocontent062015","status":"publish","type":"post","link":"https:\/\/bel.azbuki.bg\/en\/matematics\/matharticles\/mathinfocontent062015\/","title":{"rendered":"Mathematics and Informatics, Number 6\/2015, Volume 58"},"content":{"rendered":"


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

 <\/p>\n

EDUCATIONAL MATTERS \/\u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e<\/strong><\/p>\n

Errors Related to Topics in Geometry, Data Representation and Analysis Madeby Fifth Grade Students in the Republic of \u041cacedonia <\/a> \/
Metodi Glavche, Risto Mal\u010deski, Katerina Anevska – 567 <\/p>\nLog in to read the full text<\/a>\n

 <\/p>\n

Mathematical Skills are Required in the Changing World <\/a>\/
Desislava Georgieva – 582 <\/p>\nLog in to read the full text<\/a>\n

 <\/p>\n

EDUCATIONAL RESEARCH \/\u041d\u0410\u0423\u0427\u041d\u041e\u2013\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418<\/strong><\/p>\n

\u0418\u0441\u0442\u043e\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u0440\u0435\u0434\u043f\u043e\u0441\u0442\u0430\u0432\u043a\u0438 \u0437\u0430 \u0441\u043c\u044f\u0442\u0430\u043d\u0435\u0442\u043e \u0441 \u043f\u0440\u044a\u0441\u0442\u0438 \u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0441\u044a\u0441 \u0441\u043f\u0435\u0446\u0438\u0430\u043b\u043d\u0438 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0438 \u043f\u043e\u0442\u0440\u0435\u0431\u043d\u043e\u0441\u0442\u0438
[Historical Prerequisites for Finger Math and the Mathematics Education ofStudents with Special Educational Needs]<\/a> \/
\u041c\u0438\u043b\u0435\u043d \u0417\u0430\u043c\u0444\u0438\u0440\u043e\u0432 \/ Milen Zamfirov – 593 <\/p>\nLog in to read the full text<\/a>\n

 <\/p>\n

One more Proof for the Distance Between the Incentre and the Orthocentre ofthe Triangle <\/a>\/
\u0160efket Arslanagi\u0107 – 604 <\/p>\nLog in to read the full text<\/a>\n

 <\/p>\n

Computer Discovered Mathematics: Pedal Corner Products <\/a>\/
Sava Grozdev, Deko Dekov – 609 <\/p>\nLog in to read the full text<\/a>\n

 <\/p>\n

E\u0434\u043d\u043e \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u043e\u0440\u0442\u043e\u0446\u0435\u043d\u0442\u0440\u0438\u0447\u043d\u0438\u044f \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a [A Generalization of theOrthocentric Triangle] <\/a>\/
\u0425\u0430\u0438\u043c \u0425\u0430\u0438\u043c\u043e\u0432 – 616<\/p>\nLog in to read the full text<\/a>\n

 <\/p>\n

\u0422\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u0424\u043e\u043d\u0442\u0435\u043d\u0435 \u043f\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u043d\u0430 \u043e\u043f\u0438\u0441\u0430\u043d\u0438 \u0446\u0435\u043d\u0442\u0440\u0430\u043b\u043d\u0438 \u043a\u043e\u043d\u0438\u0447\u043d\u0438\u0441\u0435\u0447\u0435\u043d\u0438\u044f
[Fonten\u00e9 Theorem with Respect to Surcumscribed Central Conics] <\/a>\/
\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 – 621 <\/p>\nLog in to read the full text<\/a>\n

 <\/p>\n

CONTEST PROBLEMS \/\u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong><\/p>\n

\u041a\u043e\u043d\u043a\u0443\u0440\u0441\u043d\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0431\u0440\u043e\u044f [Contest Problems of the Issue]  – 639<\/p>\nLog in to read the full text<\/a>\n

 <\/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, 2015
[Solutions of the ContestProblems from Issue 1, 2015] – 640<\/p>\nLog in to read the full text<\/a>\n

 <\/p>\n

MATHEMATICAL EDUCATION WORLDWIDE\/\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u0415\u0421\u041a\u041e\u0422\u041e \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u041d\u0418\u0415 \u041f\u041e \u0421\u0412\u0415\u0422\u0410<\/strong><\/p>\n

\u0413\u0435\u043d\u0438\u0439 \u0441 \u0431\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u0438 \u043f\u0440\u043e\u0438\u0437\u0445\u043e\u0434 [Genius with Bulgarian Origin] \/
\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432 \/ Sava Grozdev – 643 <\/p>\nLog in to read the full text<\/a>\n

 <\/p>\n

ANNUAL CONTENTS \/ \u0413\u041e\u0414\u0418\u0428\u041d\u041e \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong> – 652<\/p>\n

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READ IN THE LATEST ISSUES OF \u201eAZ BUKI\u201c JOURNALS \/
\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>– 657<\/p>\n

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GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u0415 \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/strong> – 659<\/p>\n

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

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 <\/p>\n

 <\/a> ERRORS RELATED TO TOPICS IN GEOMETRY, DATA REPRESENTATION AND ANALYSIS MADEBY FIFTH GRADE STUDENTS IN THE REPUBLICOF MACEDONIA<\/strong><\/p>\n

 <\/p>\n

1<\/sup>Metodi Glavche, 2<\/sup>Risto Mal\u010deski, 3<\/sup>Katerina Anevska<\/strong><\/p>\n

1<\/sup>Ss. Cyril and Methodius University \u2013 Skopje<\/p>\n

2,3<\/sup>FON University \u2013 Skopje<\/p>\n

 <\/p>\n

Abstract.<\/strong> In the learning process it is natural for omissions to occur and if they arenot identifi ed and eliminated in a timely manner, they are multiplied further on in thecourse of education. Therefore, one of the tasks of the mathematics instruction is todetect the errors made by the students and to eliminate them on time. Errors that havemade students from fi fth grade in arithmetic and algebra are processed in (Glavche,Mal\u010deski & Anevska, 2015). In this paper the results of the research are presentedabout some of the most prominent errors that fi fth grade students in the Republic ofMacedonia make. Additionally, the paper offers a systematic overview of the identifi ederrors and the reasons for their occurrence. It also offers procedures for elimination ofthe identifi ed errors.Keywords: data, error, fi fth grade, geometry, student<\/p>\n

 <\/p>\n

Dr. Metodi Glavche, Assoc. Prof<\/strong><\/p>\n

Faculty of Pedagogy<\/p>\n

Ss. Cyril and Methodius University<\/p>\n

Skopje, Macedonia<\/p>\n

 <\/p>\n

Prof. Risto Mal\u010deski, DSc<\/strong><\/p>\n

Faculty of Informatics<\/p>\n

FON University<\/p>\n

Skopje, Macedonia<\/p>\n

 <\/p>\n

Dr. Katerina Anevska, Assoc. Prof.<\/strong><\/p>\n

Faculty of Informatics<\/p>\n

FON University<\/p>\n

Skopje, Macedonia<\/p>\n

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

\n

 <\/p>\n

 <\/a>MATHEMATICAL SKILLS ARE REQUIREDIN THE CHANGING WORLD<\/strong><\/p>\n

 <\/p>\n

Desislava Georgieva<\/strong><\/p>\n

University of Ruse \u201cAngel Kanchev\u201d <\/p>\n

\u201cIn mathematics, know-how is more important than mere possession of information.\u201d<\/p>\n

George P\u00f3lya<\/p>\n

 <\/p>\n

Abstract.<\/strong> Different treatments of the notions \u201cskill\u201d and \u201cmathematical skill\u201d arepresented in the paper with regard to their relation to the notion of competence. Old andnew educational standards of different countries are collected and analysed, thus outliningthe framework of the mathematical skills which are necessary to face the needs ofthe 21st century education.<\/p>\n

Keywords: mathematical skill, competence, iceberg model, KSAVE model.<\/p>\n

 <\/p>\n

Mrs. Desislava Georgieva, PhD student<\/strong><\/p>\n

Department of Mathematics<\/p>\n

University of Ruse \u201cAngel Kanchev\u201d<\/p>\n

8, Studentska Str.<\/p>\n

7017 Ruse, Bulgaria<\/p>\n

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

\n

 <\/p>\n

 <\/a>\u0418\u0421\u0422\u041e\u0420\u0418\u0427\u0415\u0421\u041a\u0418 \u041f\u0420\u0415\u0414\u041f\u041e\u0421\u0422\u0410\u0412\u041a\u0418 \u0417\u0410\u0421\u041c\u042f\u0422\u0410\u041d\u0415\u0422\u041e \u0421 \u041f\u0420\u042a\u0421\u0422\u0418\u0418 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410 \u041d\u0410\u0423\u0427\u0415\u041d\u0418\u0426\u0418\u0421\u042a\u0421 \u0421\u041f\u0415\u0426\u0418\u0410\u041b\u041d\u0418 \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418\u041f\u041e\u0422\u0420\u0415\u0411\u041d\u041e\u0421\u0422\u0418<\/strong><\/p>\n

 <\/p>\n

Milen Zamfirov<\/strong><\/p>\n

Sofia University<\/p>\n

 <\/p>\n

Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430 \u0438\u0441\u0442\u043e\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0442\u043e \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 \u0441\u043c\u044f\u0442\u0430\u043d\u0435\u0442\u043e \u0441 \u043f\u0440\u044a\u0441\u0442\u0438,\u043a\u0430\u0442\u043e \u0430\u043a\u0446\u0435\u043d\u0442\u0438\u0440\u0430 \u0432\u044a\u0440\u0445\u0443 \u0432\u044a\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438\u0442\u0435 \u0437\u0430 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0441\u044a\u0441\u0441\u043f\u0435\u0446\u0438\u0430\u043b\u043d\u0438 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0438 \u043f\u043e\u0442\u0440\u0435\u0431\u043d\u043e\u0441\u0442\u0438, \u043e\u0441\u043e\u0431\u0435\u043d\u043e \u043d\u0430 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0441 \u0443\u0432\u0440\u0435\u0434\u0435\u043d \u0441\u043b\u0443\u0445. \u0412\u0437\u0435\u0442\u0438\u0441\u0430 \u043f\u043e\u0434 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u0438 \u0434\u0440\u0443\u0433\u0438 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0441 \u043d\u0430\u0440\u0443\u0448\u0435\u043d\u0438\u044f \u043a\u0430\u0442\u043e \u0434\u0438\u0441\u043a\u0430\u043b\u043a\u0443\u043b\u0438\u044f \u0438 \u0430\u0443\u0442\u0438\u0437\u044a\u043c, \u0430 \u0442\u0430\u043a\u0430\u0441\u044a\u0449\u043e \u0438 \u0443\u0447\u0435\u043d\u0438\u0446\u0438 \u0431\u0435\u0437 \u043d\u0430\u0440\u0443\u0448\u0435\u043d\u0438\u044f.<\/p>\n

Keywords: fi nger Math, mathematics education, disability, hearing loss, dyscalculia,autism<\/p>\n

 <\/p>\n

HISTORICAL PREREQUISITES FOR FINGER MATH AND THEMATHEMATICS EDUCATION OF STUDENTS WITH SPECIALEDUCATIONAL NEEDS<\/strong><\/p>\n

 <\/p>\n

Abstract.<\/strong> This article overviews the historical development of fi nger Math accentingon the possibilities for its implication in the teaching process of students with specialeducational needs, namely students with hearing loss. Other students with disabilities likedyscalculia and autism are taken under consideration and also students without disabilities.<\/p>\n

 <\/p>\n

Dr. Milen Zamfi rov, Assoc. Prof.<\/strong><\/p>\n

Department of Special Education and Speech Therapy<\/p>\n

Sofi a University<\/p>\n

15, Tsar Osvoboditel Blvd.<\/p>\n

1504 Sofi a, Bulgaria<\/p>\n

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

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 <\/a>ONE MORE PROOF FOR THE DISTANCEBETWEEN THE INCENTRE ANDTHE ORTHOCENTRE OF THE TRIANGLE<\/strong><\/p>\n

 <\/p>\n

\u0160efket Arslanagi\u0107<\/strong><\/p>\n

University of Sarajevo<\/p>\n

 <\/p>\n

Abstract.<\/strong> One more proof is proposed in the present paper concerning the thedistance between the incentre (I) and the orthocentre (H) of the triangle.Keywords: distance, incentre, orthocentre, sine law, cosine law, centroid of atriangle.<\/p>\n

 <\/p>\n

Prof. Dr. \u0160efket Arslanagi\u0107<\/strong><\/p>\n

Faculty of Mathematics and Natural Sciences<\/p>\n

University of Sarajevo<\/p>\n

Sarajevo, Bosna and Herzegovina<\/p>\n

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

\n

 <\/p>\n

 <\/a>COMPUTER DISCOVERED MATHEMATICS:PEDAL CORNER PRODUCTS<\/strong><\/p>\n

1<\/sup>Sava Grozdev, Deko Dekov<\/strong><\/p>\n

1<\/sup>University of Finance, Business and Entrepreneurship<\/p>\n

 <\/p>\n

Abstract.<\/strong> Theorems about pedal corner products obtained by the computer program\u201cDiscoverer\u201d are presented in the paper. 2010 Mathematics Subject Classifi cation:Primary 51-04, 68T01, 68T99.<\/p>\n

Keywords: pedal corner product, triangle geometry, remarkable point, computerdiscovered<\/p>\n

mathematics, Euclidean geometry, Discoverer.<\/p>\n

 <\/p>\n

Prof. Sava Grozdev, DSc<\/strong><\/p>\n

University of Finance, Business and Entrepreneurship<\/p>\n

1, Gusla Street<\/p>\n

1618 Sofi a, Bulgaria<\/p>\n

 <\/p>\n

Dr. Deko Dekov, Assoc. Prof.<\/strong><\/p>\n

81, Zahari Knjazheski Street<\/p>\n

6000 Stara Zagora, Bulgaria<\/p>\n

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

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 <\/a>E\u0414\u041d\u041e \u041e\u0411\u041e\u0411\u0429\u0415\u041d\u0418\u0415\u041d\u0410 \u041e\u0420\u0422\u041e\u0426\u0415\u041d\u0422\u0420\u0418\u0427\u041d\u0418\u042f \u0422\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u041a<\/strong><\/p>\n

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\u0425\u0430\u0438\u043c \u0425\u0430\u0438\u043c\u043e\u0432<\/strong><\/p>\n

 <\/p>\n

Abstract.<\/strong> \u0410\u0432\u0442\u043e\u0440\u044a\u0442 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u043e\u0440\u0442\u043e\u0446\u0435\u043d\u0442\u0440\u0438\u0447\u043d\u0438\u044f \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a. \u041e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u044f\u0442 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u0435 \u043f\u0435\u0440\u0441\u043f\u0435\u043a\u0442\u0438\u0432\u0435\u043d \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 ABC \u0438 \u0437\u0430\u0432\u0438\u0441\u0438 \u043e\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u043d\u0430\u0442\u043e\u0447\u043a\u0430 \u043d\u0430 \u0427\u0435\u0432\u0430 P . \u041d\u0430\u0440\u0438\u0447\u0430\u043c\u0435 \u0433\u043e H \u2212 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u043d\u0430 \u0442\u043e\u0447\u043a\u0430\u0442\u0430 P . \u0418\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435\u0442\u043e,\u043a\u043e\u0435\u0442\u043e \u043d\u0430 \u0442\u043e\u0447\u043a\u0430 \u043d\u0430 \u0427\u0435\u0432\u0430 P \u0441\u044a\u043f\u043e\u0441\u0442\u0430\u0432\u044f \u043f\u0435\u0440\u0441\u043f\u0435\u043a\u0442\u043e\u0440\u0430 \u043d\u0430 H \u2212 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 \u043d\u0430 P \u0438\u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 ABC , \u043d\u0430\u0440\u0438\u0447\u0430\u043c\u0435 H \u2212 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 P . \u041f\u043e\u043a\u0430\u0437\u0432\u0430\u043c\u0435, \u0447\u0435 H \u2212 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435\u0442\u043e \u0435 \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044f \u043d\u0430 \u0434\u0432\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0438 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0432\u0430\u043d\u0438\u044f \u043d\u0430 \u0442\u043e\u0447\u043a\u0438: \u0434\u043e\u043f\u044a\u043b\u043d\u0435\u043d\u0438\u0435\u0438 \u0438\u0437\u043e\u0433\u043e\u043d\u0430\u043b\u043d\u0430 \u0441\u043f\u0440\u0435\u0433\u043d\u0430\u0442\u043e\u0441\u0442. \u041d\u0430\u043c\u0438\u0440\u0430\u043c\u0435 \u043e\u0431\u0440\u0430\u0437\u0438\u0442\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u0437\u0430\u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0435\u043b\u043d\u0438 \u0442\u043e\u0447\u043a\u0438 \u043f\u0440\u0438H \u2212 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435\u0442\u043e. \u0420\u0435\u0437\u0443\u043b\u0442\u0430\u0442\u0438\u0442\u0435 \u0432 \u0442\u0430\u0437\u0438 \u0441\u0442\u0430\u0442\u0438\u044f \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0431\u044a\u0434\u0430\u0442 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0438 \u0437\u0430 \u0442\u0435\u0441\u0442\u0432\u0430\u043d\u0435 \u043d\u0430 \u043a\u043e\u043c\u043f\u044e\u0442\u044a\u0440\u043d\u0430\u0442\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u201e\u041e\u0442\u043a\u0440\u0438\u0432\u0430\u0442\u0435\u043b\u201c.<\/p>\n

Keywords: generalization of the orthic triangle, perspective triangle, perspector, notable points<\/p>\n

 <\/p>\n

A GENERALIZATIONOF THE ORTHOCENTRIC TRIANGLE<\/strong><\/p>\n

Abstract.<\/strong> The author proposes a generalization of the orthic triangle. Thegeneralized triangle is defi ned by an arbitrary point of Ceva P and it is in perspectivewith the reference triangle ABC . We call it the H \u2212 triangle of point P . We call theH \u2212 transform of point P the mapping which assigns to point P the perspector ofthe H \u2212 triangle of point P and triangle ABC . We show that the H \u2212 transform iscomposition of two known transforms: the complement and the isogonal conjugate. Weidentify the images of a few remarkable points under the H \u2212 transform. The results inthis paper could be used for testing of the computer program \u201cDiscoverer\u201d.<\/p>\n

 <\/p>\n

Haim Haimov<\/strong><\/p>\n

16, Bratia Shkorpil Str.<\/p>\n

9000 Varna, Bulgaria<\/p>\n

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

\n

 <\/p>\n

 <\/a>\u0422\u0415\u041e\u0420\u0415\u041c\u0410\u0422\u0410 \u041d\u0410 \u0424\u041e\u041d\u0422\u0415\u041d\u0415 \u041f\u041e \u041e\u0422\u041d\u041e\u0428\u0415\u041d\u0418\u0415\u041d\u0410 \u041e\u041f\u0418\u0421\u0410\u041d\u0418 \u0426\u0415\u041d\u0422\u0420\u0410\u041b\u041d\u0418 \u041a\u041e\u041d\u0418\u0427\u041d\u0418\u0421\u0415\u0427\u0415\u041d\u0418\u042f<\/strong><\/p>\n

1<\/sup>\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, 2<\/sup>\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432<\/strong><\/p>\n

1<\/sup>VUZF University<\/p>\n

2<\/sup>\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u041b\u043e\u0432\u0435\u0447<\/p>\n

 <\/p>\n

Abstract.<\/strong> \u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0441\u0442\u0430\u0442\u0438\u044f \u0435 \u043e\u043f\u0438\u0441\u0430\u043d\u043e \u0435\u0434\u043d\u043e \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0437\u0430\u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0435\u043b\u043d\u0430\u0442\u0430\u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043d\u0430 \u0424\u043e\u043d\u0442\u0435\u043d\u0435 \u043e\u0442 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f\u0442\u0430 \u043d\u0430 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430.<\/p>\n

Keywords: triangle, conic, pedal circle, pedal curve, Feuerbach confi guration, Eulercurve.<\/p>\n

 <\/p>\n

FONTEN\u00c9 THEOREM WITH RESPECTTO SURCUMSCRIBED CENTRAL CONICS<\/strong><\/p>\n

 <\/p>\n

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

 <\/p>\n

Abstract.<\/strong> A generalization of the remarkable Fonten\u00e9 theorem from the geometry oftriangle is described in the present paper.<\/p>\n

 <\/p>\n

Prof. Sava Grozdev, DSc<\/strong><\/p>\n

University of Finance, Business and Entrepreneurship<\/p>\n

1, Gusla Str.<\/p>\n

1618 Sofi a, Bulgaria<\/p>\n

 <\/p>\n

Dr. Veselin Nenkov, Assoc. Prof.<\/strong><\/p>\n

Technical College Lovech<\/p>\n

31, Sajko Saev Str.<\/p>\n

Lovech, Bulgaria<\/p>\n

 <\/p>\n

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

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

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

CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415   EDUCATIONAL MATTERS \/\u0412\u042a\u041f\u0420\u041e\u0421\u0418 \u041d\u0410 \u041f\u0420\u0415\u041f\u041e\u0414\u0410\u0412\u0410\u041d\u0415\u0422\u041e Errors Related to Topics in Geometry, Data Representation and Analysis Madeby Fifth Grade Students in the Republic of \u041cacedonia \/ Metodi Glavche, Risto Mal\u010deski, Katerina Anevska – 567    Mathematical Skills are Required in the Changing World \/ Desislava Georgieva – 582    EDUCATIONAL RESEARCH \/\u041d\u0410\u0423\u0427\u041d\u041e\u2013\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 […]<\/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 LVIII, 2015 - 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