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• WMI2: interactive mathematics on the web

  393-405

  Zoltán Kovács

  Views:

  135

  After 5 years of experiments and feedback we decided to continue the software development on WebMathematics Interactive, a web-based e-learning tool, rewriting it from scratch. The demonstration version of WebMathematics Interactive 2 (WMI2) has been shown to the expert audience on the CADGME conference. In this article we summarize the development goals and results.

• Maximum and minimum problems in secondary school education

  81-98

  Zsolt Fülöp

  Views:

  164

  The aim of this paper is to offer some possible ways of solving extreme value problems by elementary methods with which the generally available method of differential calculus can be avoided. We line up some problems which can be solved by the usage of these elementary methods in secondary school education. The importance of the extremum problems is ignored in the regular curriculum; however they are in the main stream of competition problems – therefore they are useful tools in the selection and development of talented students. The extremum problem-solving by elementary methods means the replacement of the methods of differential calculus (which are quite stereotyped) by the elementary methods collected from different fields of Mathematics, such as elementary inequalities between geometric, arithmetic and square means, the codomain of the quadratic and trigonometric functions, etc. In the first part we show some patterns that students can imitate in solving similar problems. These patterns could also provide some ideas for Hungarian teachers on how to introduce this topic in their practice. In the second part we discuss the results of a survey carried out in two secondary schools and we formulate our conclusion concerning the improvement of students' performance in solving these kind of problems.

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

  255-267

  Lajos Klukovits

  Views:

  154

  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.

• On two long lasting delusions in the history of equations

  147-158

  Lajos Klukovits

  Views:

  120

  Almost everybody was thought, that the 9th century Moshlem mathematician al-Khwarismi was the inventor of two powerful methods – called by him as al-jabr and al-muqabala – in solving quadratic equations. The second belief is that between Leonardo's Liber abaci and Luca Pacioli's Summa... happened nothing interesting in algebra. We will show that both beliefs are false by giving examples from the antiquity and analyzing Mediaeval Italian manuscripits.