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

  337-355

  László Filep

  Views:

  34

  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.

• Constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of CAS

  363-376

  Muharrem Aktümen

  Tolga Kabaca

  Views:

  26

  Calculus concepts should have been taught in a carefully designed learning environment, because these concepts constitute a very important base for almost all applied sciences. The integral, one of the fundamental concepts of Calculus, has a wide application area. This paper focuses on constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of a CAS.
  In this study, a semi-structured interview was carried out. In this interview, we tried to construct the disk method formula.
  The levels of constructing the disk method formula in this study are:
  • Introducing the concept: evaluating the volume of an Egyptian pyramid.
  • Evaluating the volume of a cone obtained by revolution (using Maple worksheet).
  • Designing their own ring and evaluating its price (using Maplet).
  In this study, the interview has been presented as a dialog between teacher and students. When we look at feedback from students, we see that such a teaching method effects students in a positive way and causes them to gain conceptual understanding directed towards the concepts of approximation and volume.

• On the past of a famous theorem: the predecessors of a theorem of Pythagoras

  255-267

  Lajos Klukovits

  Views:

  32

  The well-known Theorem of Pythagoras asserts a relation among the sides of any right-angled triangle. It can be found any secondary school textbook. An interesting question whether this result due to the Pythagoreans from the VIth century BC, or it was known in earlier civilizations. The first answer is a vague yes. According to the legends the Egyptian rope-stretchers used a triangle with sides 3,4,5 units to create right angle. But are there real evidences that this result was known earlier? We will argue that in almost all river-valley civilizations it was known and used.