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• Über ähnliche Aufsatzdreiecke einer Strecke

  337-348

  Oswald Giering

  Views:

  8

  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.

• Besondere Punkte der Euler-Geraden

  145-157

  Oswald Giering

  Views:

  5

  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.

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

  49-65

  Oswald Giering

  Views:

  13

  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.

• Zur Visualisierung des Satzes von Pythagoras

  217-228

  Oswald Giering

  Views:

  3

  In this article we make a study of a not-classical visualization of the theorem of Pythagoras using methods of elementary school geometry. We find collinear points, copoint straight lines and congruent pairs of parallelograms. The configuration of their midpoints induces a six-midpoint and a four-midpoint theorem.