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

  255-267

  Lajos Klukovits

  Views:

  129

  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 four-dimensional crystallographic groups

  391-404

  Eszter Horváth

  Views:

  99

  In his paper [12] S. S. Ryshkov gave the group of integral automorphisms of some quadratic forms (according to Dade [6]). These groups can be considered as maximal point groups of some four-dimensional translation lattices in E^4. The maximal reflection group of each point group, its fundamental domain, then the reflection group in the whole symmetry group of the lattice and its fundamental domain will be discussed. This program will be carried out first on group T. G. Maxwell [9] raised the question whether group T was a reflection group. He conjectured that it was not. We proved that he had been right. We shall answer this question for other groups as well. Finally we shall give the location of the considered groups in the tables of monograph [4]. We hope that our elementary method will be useful in studying linear algebra and analytic geometry. Futhermore, 4-dimensional geometry with some visualisation helps in better understanding important concepts in higher-dimensional mathematics, in general.

• Report on the "English Language Section of Varga Tamás Days 2009"

  169-175

  Krisztina Barczi

  Views:

  103

  The 9th English Language Section as a part of the Varga Tamás Days was organised by the Department of Mathematics Education at the Teacher Training Institute of the Eötvös Loránd University. We report on the talks and the following discussions in this section.