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• Packings in hyperbolic geometry

  209-229

  H. Zeitler

  Views:

  21

  I am becoming older. That's why I am returning to my youth sins. "On revient toujours á ses premiers amoures". This sin was the noneuclidean hyperbolic geometry – especially the Poincaré model. I was teaching this kind of geometry over many years as well in highschool (Gymnasium) as for beginners at the university too.
  A lot of results concerning packings in hyperbolic geometry are proved by the Hungarian school around László Fejes Tóth. In this paper we construct very special packings and investigate the corresponding densities. For better understanding we are working in the Poincaré model. At first we give a packing of the hyperbolic plane with horodisks and calculate the density. In an analogous way then the hyperbolic space is packed by horoballs. In the last case the calculation of the density is a little bit difficult. Finally it turns out that in both cases the maximal density is reached.

• Hyperbolische 5-Rechtecke

  111-123

  H. Zeitler

  Views:

  24

  The main topic of this paper is the investigation of 5-pentagons whose interior angles are all right angles within the hyperbolic geometry (so-called 5-rectangles). Some knowledge of elementary hyperbolic geometry is required.
  At first the existence of such a polygon is shown by construction within the Kleinmodel. Then two formulas due to D. M. Y. Sommerville [3] are proved. This means to juggle with trigonometric formulas of hyperbolic geometry.
  In the last years a big number of papers concerning hyperbolic geometry was published. This proves that the interest in this nice discipline is growing again.

• Improper integrals, an excursion to classical calculus

  303-317

  Herbert Zeitler

  Views:

  28

  The aim of this paper is to show in what way we investigated improper integrals in the classroom. It was very important to calculate explicitly a lot of examples. Doing so, a criterion was developed. With step curves and infinite series we had a quick look at the mathematical background. The shot in the universe showed that improper integrals are needed in physics.

• Reflecting upon reflections

  1-12

  H. Zeitler

  D. Camp

  Views:

  8

  This paper considers many applications of reflections in geometry. It begins with a few motivational problems for the classroom and goes on to consider the formal application to cases involving reflections across one line, two lines and three lines. It wraps up with a summary of results for reflections in higher orders.
  All this stuff was treated in German and American schools too – so the paper is a typical example of German-American didactics.
  "Thinking is one of the greatest pleasure of mankind." – Galileo Galilei

• Miscellaneous topics in finite geometry: in memory of Professor Dr. Ferenc Kárteszi (1907-1989)

  255-275

  Herbert Zeitler

  Views:

  33

  The article starts with a short introduction to finite (K,L)-geometry. Then a lot of counting propositions is given and proved. Finally the famous theorem of Miquel is investigated in classical and in finite geometry. At the end of the article there is a call to all readers: Don't forget (finite) geometry and don't forget the outstanding geometer Prof. Dr. F. Kárteszi!