THE MINISTRY OF EDUCATION, RESEARCH, YOUTH AND SPORTS,
"TRANSILVANIA" UNIVERSITY FROM BRASOV
THE FACULTY OF MATHEMATICS AND INFORMATICS
BRASOV SCHOOL INSPECTORATE
THE TECHNICAL "MIRCEA CRISTEA” FROM BRASOV
THE NATIONAL COLLEGE "ÁPRILY LAJOS” FROM BRASOV
M.E.C.T.S.
No.......... /............
The Faculty of Mathematics and Informatics
"Transilvania" University Brasov
No. ................/....................
The Brasov School Inspectorate
No. ............./...................
The Technical College "Mircea
The National College "Áprily
Cristea” Brasov
Lajos”Brasov
No.............../.............
No. ............./..............
The "Christian Kertsch" Association
The International Association József Wildt
No:21./12.10.2012
No 37./12.10.2012
Organizes:
THE INTERNATIONAL CONFERENCE:
MATHEMATICAL EDUCATION IN THE CURRENT EUROPEAN CONTEXT
THIRD EDITION
taking place under the aegis of
 The Society of Mathematical Sciences from Romania, the Brasov
branch
 The Faculty of Mathematics and Informatics from the
"Transilvania" University from Brasov
 The Brasov School Inspectorate
 The Scientific Association József Wildt
 The Christian Kertsch Association
Distinguished guests:
- Professor Emil Stoica, PhD pro-rector at "Transilvania" University from Brasov
- TeacherBucur Ariana, General School Inspector at the Brasov School Inspectorate
- Teacher Mária Szabó, Assistant to the General School Inspector at Brasov School
Inspectorate
Scientific Committee:
- University lecturer Eugen Păltănea, PhD at the Faculty of Mathematics and
Informatics, "Transilvania" University from Brasov
- Teacher Cozeta Ţion, Expert Inspector at the Brasov School Inspectorate
Project team:
Coordinators:
- Teacher Mihaly Bencze - The National College "Áprily Lajos” from Brasov
- Teacher Virginia Marinescu - The Technical College "Mircea Cristea” Brasov
Organizers:
- Teacher Camelia Moldovan - The Technical College "Mircea Cristea”
- Teacher Goran Angelica- The Technical College "Mircea Cristea”
- Teacher Felicia Mereuţă - The Technical College "Mircea Cristea”
- Teacher Negrea Camelia- The Technical College "Mircea Cristea”
- Teacher Anca Popa Alexandru - The "Petru Rares” College
- Teacher Stancu Diana – The Technical College "Mircea Cristea”
- Teacher Cristina Centea - The Technical College "Mircea Cristea”
- Teacher Daniela Andreiu - The Technical College "Mircea Cristea”
- Administrator Bogdan Barbu
The motivation of the project:
„Learning Mathematics, one learns to think”
Grigore C. Moisil
Romania's affiliation to the European Union involves harmonizing the Romanian
educational system with the other European educational systems. The Program of Bologna traced
common development directions for the university education and it is now necessary to find
essential landmarks in the pre-university education as well as to form the young.
The suggested event will allow useful experience exchanges in the field of interactive
teaching strategies and that of integrating multimedia technologies during the Mathematics
classes. We aim at promoting the innovative teaching measures, at encouraging actions which
allow the insurance of quality in education and the life-long constant professional training.
Mathematics is an essential subject in forming a young person. The actions dedicated to
" Mathematical education in the current European context 2012" allow certain ideas to be known.
They also allow the knowledge of certain teaching-learning approaches of this subject in schools
and they should be known by our teachers and students.
The Objectives:
 Knowing the place held by Mathematics in the curriculum of different schools
 Promoting modern methods of teaching, learning and assessment (including the
computer-assisted learning)
 Motivating teachers and students to use the interactive teaching methods and
strategies which are specific to modern pedagogy
 Motivating teachers and students for a serious scientific training in the field of
professional competences.
Target group: teachers from elementary schools, from high schools, beginner
teachers,students and senior students, people working on an M.A. and a Ph.D. within the
Mathematical faculties.
The suggested sections:
 Section I: Relevant aims/competences and contents for the Mathematical
education of the young in Romanian and European Schools
 Section II: Computer assisted Mathematics lessons
 Section III: Themes, problems, Mathematical lessons - innovative and
interdisciplinary
approaches
(contents,
strategies,
methods
and
approaching/solving techniques)
 Section IV: a)-for teachers/Mathematics and its connections with other fields of
study
 b)-for pupils - a team of two pupils and one guiding teacher/ Mathematics and its
connections with other fields of study
Location: The National College “Áprily Lajos”, 3, Dupa Ziduri Street, Brasov
Date: 23.11.2012
Participation Rules:
a. Sending the paper and the registration form (see Appendix 1, deadline 20.11.2012 for the
papers and 16.11.2012 for the registration form) to the contact persons.
The contact persons are:
1. Teacher Camelia Moldovan, phone no.: 0040 744 321 716, e-mail:
camelia.moldovan@yahoo.com (Part 1)
2. Teacher Anca Alexandru Popa, phone no.: 0040 723 068 360, e-mail:
anca_popa4@yahoo.com, (Part 2)
3.
Teacher
Angelica
Goran,
phone
no.0040
748053794,
e-mail
angelica_goran@yahoo.com ; (Part 3)
4. Teacher Mereuţă Felicia, phone no. 0040 729154752 / 0040 729988888, e-mail
adyfely@yahoo.com (Part 4 teachers) and teacher Stancu Diana phone no 0040
753019033 , e-mail diannnas@yahoo.com ( part 4 pupils)
5. Teacher Mihaly Bencze: benczemihaly@gmail.com and 6. Teacher Marinescu
Virginia gini_l18@yahoo.com (the responsible persons for the Conference)
The papers, written in the format shown in the appendix, will be sent on the symposium email: international.conference.brasov@gmail.com Valuable materials in electronic
format, may contribute to the creation of an ISBN volume, on this topic. Each paper can have
maximum three authors.
b. The participation fee is 55 Ron/paper/author [please read point c) of the participation rules].
The fee must be sent until October 16th 2012 at this address: ASOCIAŢIA CHRISTIAN
KERTSCH, in the account RO76BRDE080SV84870500800 (please mention „for
Conference 2012”), or it can be paid in the conference day. The fee for students who
participate at the symposium is 30 Ron. Foreign participants must send the equivalent of 25
Euro/teacher and 10 Euro/student. The sum covers the expenses for the printing of the
Symposium portfolio, the participation diploma, the printing of the ISBN volume and the
protocol.
c. In order to prove the payment you need to send a copy of the receipt by e-mail; (on the
address of the "Mircea Cristea " college, No. 3, Turnului Street, Brasov) and to send scanned
copies of your receipts by e-mail to the contact persons. The persons who do not attend the
Symposium directly, need webcam, microphone and an internet connection and contact our
coleague Bogdan Barbu at bogdan.cyecorp@yahoo.com on 16.11.2012 for testing the
videoconference mode/phone no. : 0040 724 766 556. All the participants from the city
and district of Brasov are asked to be present at the Conference.
d. The material will be sent in electronic format MS Word („doc” or “docx” format) in
Romanian (with abstract in English) or in English. The paper should have the following
specifications:
MsWord 2007, page format Custom size 6.73 ̎ and 9.37 ̎(
International B5), Justifiy, font: Times New Roman, size 12, line spacing: single,
with diacritics. The mirror margins will be 2 cm/0.79 ̎, except the left/right one, that
will be 2.5cm/0.98 ̎. The paper must have an even number of pages, between 2 and
10. Bibliographical references will be included when necessary (see Appendix 2). The
abstract in English will have a maximum of 15 lines, TNR font, size 11, Italics (see appendix
2, with the template for the paper).
e. For any question, please write to one of the contact persons. For accommodation, read
carefully the registration form and write to the contact persons indicated.
Assessment.
All papers will be mentioned in the catalogue of the Conference. The participants will receive
directly/by mail the diploma, the portfolio with the schedule of the activities, the catalogue and
the special ISBN volume (for the papers selected by the Scientific Committee).
Observation: The accommodation will be done according to appendix 1.
The Schedule of the Activities
23.11.2012
14.00-14.30
Receiving the participants and the guests. Seeing a thematic
exhibition(drawings and paintings on mathematical themes).
14.30-17.00 Presenting the papers
17.00-17.30 Conclusions and diploma handing
Dean of the Faculty of Mathematics and Informatics,
the Transilvania University from Brasov
Professor dr. Marin Marin
General School Inspector,
Teacher Bucur Ariana
Principal of the Technical College “M. Cristea”,
Teacher: Costea Gabriela
Principal of the National College “Aprily Lajos”,
Teacher: Pal Petki
The Christian Kertsch Association
President: Teacher Felicia Mereuţă
The International Association József Wildt
President: Teacher Mihály Bencze
APPENDIX 1
REGISTRATION FORM FOR THE CONFERENCE
Teaching Mathematics Within The Actual European Framework
Teachers
23.11.2012
AUTHOR:
1.SURNAME ...................................... FIRST NAME...............................
SPECIALIZATION……………………………………………………….
HOME ADDRESS…………………………………………………………
TELEPHONE NUMBER.............................................................................
E-MAIL.........................................................................................................
SCHOOL.......................................................................................................
SCHOOL ADDRESS....................................................................................
2. SURNAME ...................................... FIRST NAME...............................
SPECIALIZATION……………………………………………………….
HOME ADDRESS…………………………………………………………
TELEPHONE NUMBER.............................................................................
E-MAIL.........................................................................................................
SCHOOL.......................................................................................................
SCHOOL ADDRESS....................................................................................
TITLE OF THE PAPER................................................................................
..........................................................................................................................
SECTION: I, II, III, IV
PARTICIPATION: DIRECT/INDIRECT(VIDEOCONFERENCE)
PAPER PRESENTATION (MAXIMUM 10 MINUTES PPT/PPTX 2007): COMPUTER/LAPTOP,
VIDEOPROJECTOR, SMART BOARD, OTHERS
No.
Teacher
Gender
Accomodation
Meal
M/F
YES/NO
YES/NO
Accomodation: 1. Motel/hostel (90-195 RON/night or approx. 60-70 Euro/night); 2. Hotel (3*,
45-170 Euro/night).
In order to choose one of these options, please contact one of the following persons:
1. Mereuţă Felicia, e-mail: adyfely@yahoo.com
2. Centea Cristina, e mail: cristina_centea@yahoo.co.uk
3. Andreiu Daniela, e/mail: dscutpyt@yahoo.com
Please enclose the scanned receipt for the participation fee.
Date: ..................................................
REGISTRATION FORM FOR THE CONFERENCE
Teaching Mathematics Within The Actual European Framework
Students/Pupils
23.11.2012
AUTHOR:
1.SURNAME ...................................... FIRST NAME...............................
SPECIALIZATION………………………YEAR………………………….
HOME ADDRESS…………………………………………………………
TELEPHONE NUMBER.............................................................................
E-MAIL.........................................................................................................
UNIVERSITY......................................................................................................
UNIVERSITY ADDRESS....................................................................................
2. SURNAME ...................................... FIRST NAME...............................
SPECIALIZATION…………………………YEAR…………………………….
HOME ADDRESS…………………………………………………………
TELEPHONE NUMBER.............................................................................
E-MAIL.........................................................................................................
UNIVERSITY.......................................................................................................
UNIVERSITY ADDRESS....................................................................................
TITLE OF THE PAPER................................................................................
..........................................................................................................................
GUIDING TEACHER
SECTION: I, II, III, IV
PARTICIPATION: DIRECT/INDIRECT
PAPER PRESENTATION (MAXIMUM 10 MINUTES PPT/PPTX 2007): COMPUTER/LAPTOP,
VIDEOPROJECTOR, SMART BOARD, OTHERS
No.
Teacher
Gender
Accomodation
Meal
M/F
YES/NO
YES/NO
Accomodation: 1. Motel/hostel (90-195 RON/night or approx. 60-70 Euro/night); 2. Hotel (3*,
45-170 Euro/night).
In order to choose one of these options, please contact one of the following persons:
1. Mereuţă Felicia, e-mail adyfely@yahoo.com
2. Centea Cristina, e mail: cristina_centea@yahoo.co.uk
3. Andreiu Daniela, e/mail: dscutpyt@yahoo.com
Please enclose the scanned receipt for the participation fee and the statement of compliance
signed.
Date: ..................................................
APPENDIX 2 (paper model)
ABOUT AM-HM INEQUALITY
Mihály Bencze
Abstract
In [1] Bencze, M. introduced the following notation.
where ai > 0
(i = 1, 2, ..., n) and by mathematical induction proved that
G(m) G(m − 1) ≥ ... ≥ G(1) ≥ G(0) = n2.
In this paper we generalize this result and we give some refinements.
Main result
Theorem 1. If a, b, c > 0, then
Proof. This is a classical inequality, but now we give an elementary proof.
If x, y, z > 0, then
Using this inequality, we obtain the following
Theorem 2. If ai > 0 (i = 1, 2, ..., n) , then
Proof. We have
which is equivalent with
, therefore :
2000 Mathematics Subject Classification. 26D15.
Key words and phrases. Means, AM-GM-HM inequality
References
[1] Bencze, M., Egyenlőtlenségekről, (In Hungarian), Matematikai Lapok
(Kolozsvár), Nr. 2, 1976, pp.49-54.
[2] Octogon Mathematical Magazine (1993-2009)
[3] Bencze, M., A new proof of CBS inequality, Octogon Mathematical
Magazine, Vol. 10, Nr. 2, October 2002, pp. 841-842.
Str. Hărmanului 6, 505600 Săcele-Négyfalu, Jud. Braşov, Romania
E-mail: benczemihaly@yahoo.com
ON SOME PROPERTIES OF CYCLIC QUADRILATERAL
Nicuşor Minculete
Abstract
The aim of this paper is to present another simple proof of the Japanese
Theorem and two interesting relations.
In (see [5]), W. Reyes gave a proof of the Japanese Theorem (see
2, pp. 193) using a result due to the French geometer Victor Thébault.
Reyes mentioned that a very long proof of this theorem can be found in
(see [1], pp.125-128). In (see [6], pp. 154), P. Yiu found a simple proof of
the Japanese Theorem. Other two proofs of it can be found in books (see
[3], pp. 92) and (see [4], pp. 110).
The Japanese Theorem. Let ABCD be a convex quadrilateral inscribed
in a circle. Denote by I a ra  , I b rb  , I c rc  , I d rd  the incircles of the
triangles BCD, CDA, DAB and ABC. Prove the following:
(i) The incenters form a rectangle;
(ii) ra  rc  rb  rd .
In [3] D. Mihalca, I. Chiţescu and M. Chiriţă use the identity
r
cos A  cos B  cos C  1  , which is true in any triangle ABC, and in
R
[4]
M.
E.
Panaitopol
and
L.
Panaitopol
show
that
ra  rc  Rcos x  cos y  cos z  cos u  2  rb  rd ,
  
  
  
where R is the circumradius, m AB   2 x , m BC   2 y , m CD   2 z









and m AD   2u .


We will give below another simple proof of it.
Proof. (i) In the cyclic quadrilateral ABCD we construct the bisectors
which give the incenters of the triangles ABD, ABC and BCD (see figure
1).
2010 Mathematics Subject Classification: 51M04
Key words and phrases: cyclic quadrilateral, Japanese Theorem
References
[1] H. Fukagawa and D. Pedoe, Japanese Temple Geometry, Charles
Babbage Research Centre, Manitoba, Canada, 1989.
[2] R. A. Johnson, Advanced Euclidean Geometry, 1925, Dover reprint.
[3] D. Mihalca, I. Chiţescu and M. Chiriţă, Geometria patrulaterului,
Editura Teora, Bucureşti, 1998 (in Romanian).
[4] M. E. Panaitopol and L. Panaitopol, Probleme de geometrie rezolvate
trigonometric, Editura GIL, Zalău, 1994 (in Romanian).
[5] W. Reyes, An Application of Thébaults Theorem, Forum
Geometricorum, Volume 2(2002), 183-185.
[6] P. Yiu, Euclidean Geometry, Florida Atlantic University Lecture
Notes, 1998.
Dimitrie Cantemir University of Braşov, Department of REI, Braşov,
Romania
E-mail address: minculeten@yahoo.com
STATEMENT OF COMPLIANCE
The undersigned .................. teacher/student/pupil at ...................... declare on my sole
risk that the paper .........................., which I will present at the International Symposium
“Mathematical Education In The Current European Context” in Brasov, 23.11.2012 is
original and all the sources used are mentioned in the Bibliography.
Participant’s signature,
........................
Brasov, November 23rd 2012
Section responsible teacher,
...................................