Volume XVIII , issue 1 ( 2015 ) back
 Von der Klassifikation der Vierecke zum System der Vierecke 1$-$15 Joachim T. Haug and Carolin Haug Ludwig-Maximilians-Universität München, Biozentrum -- Department Biologie II, Groß-haderner Str. 2, 82152 Planegg-Martinsried, Deutschland

Abstract

MSC Subject Classification: G44

MathEduc Subject Classification: 97G40

 On Catalan numbers 16$-$24 Tanja Stojadinović Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

Abstract

In this article we introduce one of the most frequently encountered sequences in mathematics, the sequence of Catalan numbers. The numerous and various occurrences and applications in combinatorial problems as well as their relations with other famous numerical sequences make Catalan numbers very suitable for creative teaching of mathematics at all levels.

Keywords: Catalan numbers; binary trees; associahedron; permutations.

MSC Subject Classification: 97K20

MathEduc Subject Classification: K25

 A simple proof of the change of variable theorem for the Riemann integral 25$-$28 Haryono Tandra

Abstract

In this note, we present a simple proof of the change of variable theorem for the Riemann integral. The proof gives an alternate approach of how a class material on this topic can sistematically be carried out through a simple, succinct, and convenient way.

Keywords: Change of variable theorem; Riemann integral.

MSC Subject Classification: 97I55

MathEduc Subject Classification: I50

 On-line compendium of triangle construction problems with automatically generated solutions 29$-$44 Vesna Marinković Faculty of Mathematics, University of Belgrade, Serbia

Abstract

In this paper an on-line compendium of solutions to a class of triangle construction problems using straightedge and compass is presented. It consists of: informal description of constructions in natural-language form, formal description of constructions, illustrations of generated constructions, as well as step-by-step animations of generated constructions. This collection was generated completely automatically, using the system for automated solving of construction problems ArgoTriCS. To our knowledge this is the first automatically generated compendium of construction problems which offers solutions to almost all solvable problems from one large corpus of problems.

Keywords: Triangle construction; automatically generated solutions.

MSC Subject Classification: 97P50

MathEduc Subject Classification: P55