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• The role of computer in the process of solving of mathematical problems (results of research)

  67-80

  Henryk Kąkol

  Tadeusz Ratusiński

  Views:

  36

  We would like to present results of an almost two years investigations about the role computer in the process of solving of mathematical problems. In these investigations took part 35 students of the secondary school (generalists) in the age 17–19 years. Each of these students solved following problem:
  Find all values of the parameter m so that the function
  f(x) = |mx + 1| − |2x − m| is:
  a) bounded,
  b) bounded only from the bottom,
  c) bounded only from above,
  first without a computer and next with a special computer program. We would like to show results of these researches.

• The study of sequences defined by a first order recursion by means of a pocket calculator

  231-240

  Zoltán Tuzson

  Views:

  29

  This paper will present the way we can use a simple pocket calculator to teach mathematics. Namely, a pocket calculator can be very useful to study the properties of sequences defined by first order recursion (e.g. monotonicity, boundedness and convergence) and to gain a deeper understanding.

• Proof without words: four circles

  307-309

  Ángel Plaza

  Views:

  10

  Theorem. Let O, P and Q be three points on a line, with P lying between O and Q. Semicircles are drawn on the same side of the line with diameters OP, PQ and OQ. An arbelos is the figure bounded by these three semicircles. Draw the perpendicular…