Articles

• Packings in hyperbolic geometry

  209-229

  H. Zeitler

  Views:

  21

  I am becoming older. That's why I am returning to my youth sins. "On revient toujours á ses premiers amoures". This sin was the noneuclidean hyperbolic geometry – especially the Poincaré model. I was teaching this kind of geometry over many years as well in highschool (Gymnasium) as for beginners at the university too.
  A lot of results concerning packings in hyperbolic geometry are proved by the Hungarian school around László Fejes Tóth. In this paper we construct very special packings and investigate the corresponding densities. For better understanding we are working in the Poincaré model. At first we give a packing of the hyperbolic plane with horodisks and calculate the density. In an analogous way then the hyperbolic space is packed by horoballs. In the last case the calculation of the density is a little bit difficult. Finally it turns out that in both cases the maximal density is reached.

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• Béla Kerékjártó: (a biographical sketch)

  231-263

  György Gáll

  Views:

  30

  Kerékjártó published more than 70 scientific papers mainly in the field of topology. He achieved his most important results in the classical transformation topology and in the theoretical research of the continuous groups. He was the author of three books: Vorlesungen über Topologie; Euclidean geometry; Study on the projective geometry.

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• Statistical inference in school

  265-273

  Judit Szász-Simon

  Views:

  24

  The paper explains a classroom example for convincing students about the utility and applicability of statistical methods in learning getting people's opinions. The emphasis is on convincing instead of proving. The necessary statistical data may be obtained from the Internet as a digital text.

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  2

• Decomposition of triangles into isosceles triangles II: complete solution of the problem by using a computer

  275-300

  József Kosztolányi

  Zoltán Kovács

  Erzsébet Nagy

  Views:

  29

  We solve an open decomposition problem in elementary geometry using pure mathematics and a computer programme, utilizing a computer algebra system.

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• Synthesis of concurrent programs

  301-317

  Sándor Sike

  László Varga

  Views:

  33

  Students need a well defined method to be successful in the complex process of writing a concurrent program. In this paper we show a step by step method to create such programs. The method based on UML which has been thought to students during previous courses. UML provides standard and relatively simple tools to describe concurrent systems, and from the description the program can be derived.
  First we give a brief introduction to the concurrent systems. This is followed by the description of the method, and finally we demonstrate the method on a small problem.

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• Une modélisation d'un zoom au moyen de microscopes virtuels

  319-335

  André Antibi

  Jacques Bair

  Valérie Henry

  Views:

  34

  In this paper, we explain how a computer works when "zooms" are made around a point on a planar curve. This modelisation leads to an easy and algorithmic method to find the (vertical or not vertical) tangents for the studied curve.

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  1

• A new approach for explaining Rhind's Recto – and its utility in teaching

  337-355

  László Filep

  Views:

  38

  The Recto is a table in the Rhind Mathematical Papyrus (RMP) of ancient Egypt containing the unit fraction decompositions of fractions 2/n (3 ≤ n ≤ 101, n odd). To the question how (and why) the decompositions were made, there exists no generally accepted answer. The fact that in some other sources of Egyptian mathematics decompositions different from those in Recto exist makes the problem more difficult.
  Researchers normally try to find the answer in some formulas by which the entries of the table were calculated [see e.g. 1, 42]. We are convinced that the correct answer is not hidden in formulas but in the characteristics of Egyptian mathematics namely those of fraction and division concepts. To study them is important not only from historical point of view but also from methodological one: how to develop fraction concept and how to make division easier.

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• E-learning management systems in Hungarian higher education

  357-383

  Katalin Horváth

  Views:

  32

  Computers, informatics, and information technology have an ever-increasing role in the establishment and spread of new educational forms and methods. The role of e-learning as a new educational model is increasing in the world of computer networks, because of a widespread access to the net and a growing demand for learning beside work.
  Technological elements of e-learning can be separated as Learning Management System, authoring system, course material and a browser. Learning Management System is the software package that creates the structure of the whole educational process: course organisation, course material presentation, tracking student work, recording results, and the completion of the program.
  This publication shows examples of Learning Management Systems used in Hungarian higher education. Summarizing and systematizing expectations and demands expressed in connection with learning management systems, the present work tries to help the reader orientate on an ever-expanding market.

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  3

• Taking learning styles into consideration in e-learning based education

  385-396

  Péter Tóth

  Views:

  38

  In improving electronic teaching material processes we should take the student's learning styles or methods into consideration. The ways learners receive information may be shared into three categories (modalities): visual, auditory, kinesthetic (tactile). In this paper I present some pedagogical questions of the electronic teaching-learning environment, offer a brief survey of the different learning style theories and emphasise the importance of the modalities in encoding information. The electronic teaching material should encourage the learner to choose an appropriate form of syllabus by which his knowledge can become more efficient.

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  4

• The first clear distinction between the heuristic conjecture and the deductive proof in the ancient mathematics

  397-406

  Lajos Klukovits

  Views:

  11

  The mathematics of the ancient river-valley cultures was purely empirical, while the classical Greek mathematics was entirely deductive without any written sign of the heuristic arguments. In the forthcoming Hellenistic period there were significant changes. One of them is that in spite of the rigorous (deductive) proofs some heuristic arguments appeared in separate treatises. We show a nice example due to Archimedes.
  "We have learned from the very pioneers of this science not to have regard to mere plausible imaginings when it is a question of the reasonings to be included in our geometrical doctrine." – Proclus

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• Mechanisms for teaching introductory programming using active learning

  407-421

  Michael Wirth

  Views:

  27

  One of the requirements of teaching introductory programming to students whose branch of learning is engineering or science is bridging the gap between in-class lectures and real-world applications. Traditional passive approaches to lecturing often focus on the syntax of a language with little or no discussion of the process involved in using the language to design algorithms to solve real-world problems. One way of overcoming the limitations of traditional lecturing is by tailoring lectures towards becoming more student-oriented, a pedagogical methodology known as active learning. This paper explores mechanisms for implementing active learning in introductory programming courses in computer science.

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  1

• Proof without words: partial sum and sum of a geometric series

  423

  Ángel Plaza

  Views:

  4

  Let r be a positive real number such that 0 < r < 1, then:…

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  0