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• Über ähnliche Aufsatzdreiecke einer Strecke

  337-348

  Oswald Giering

  Views:

  28

  In this article we investigate (with methods of school geometry) a figure (PQ,ABC) consisting of three given similar triangles PQA, PQB, PQC with side PQ in common (Figure 1). We combine other triangles with this figure such as triangle ABC which is proved to be similar to the given triangles. The incircles of three additional triangles adjacent to triangle ABC will be determined.

• Classical theorems on hyperbolic triangles from a projective point of view

  175-181

  Zoltán Szilasi

  Views:

  39

  Using the Cayley-Klein model of hyperbolic geometry and the tools of projective geometry, we present elementary proofs for the hyperbolic versions of some classical theorems on triangles. We show, in particular, that hyperbolic triangles have no Euler line.

• Ein ungewöhnlicher Weg zu Jakob Steiners Umellipse eines Dreiecks und zur Steiner–Hypozykloide

  49-65

  Oswald Giering

  Views:

  21

  In real projective geometry of triangles two problems of collinear points are discussed. The problems differ only from the running through the vertices of a given triangle ABC. Resolving the problems we find two cubic curves kS and kT . Affine specialization leads to the circumscribed Steiner ellipse about the triangle ABC and shows us this ellipse in more general surroundings. Euclidean specialization leads to Steiners three-cusped hypocycloid.

• Teaching of old historical mathematics problems with ICT tools

  13-24

  Tünde Kántor

  Anna Tóth

  Views:

  20

  The aim of this study is to examine how teachers can use ICT (information and communications technology) tools and the method of blended learning to teach mathematical problem solving. The new Hungarian mathematics curriculum (NAT) emphasizes the role of history of science, therefore we chose a topic from the history of mathematics, from the geometry of triangles: Viviani's Theorem and its problem field. We carried out our teaching experiments at a secondary school with 14-year-old students. Students investigated open geometrical problems with the help of a dynamic geometric software (GeoGebra). Their research work was similar to the historical way.

• Decomposition of triangles into isosceles triangles II: complete solution of the problem by using a computer

  275-300

  József Kosztolányi

  Zoltán Kovács

  Erzsébet Nagy

  Views:

  29

  We solve an open decomposition problem in elementary geometry using pure mathematics and a computer programme, utilizing a computer algebra system.

• Besondere Punkte der Euler-Geraden

  145-157

  Oswald Giering

  Views:

  23

  In the following article the concepts "Euler line of a triangle" and "radical centre of three circles" are connected. In this way we could find some relations between special points of a triangle (orthocentre H, centre of gravity S, circumcentreM, midpoint F of the nine-point circle) and the radical centres of special triples of circles.