Szerző szerinti böngészés "Zeitler, H."

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    Packings in hyperbolic geometry
    (2004-12-01) Zeitler, H.
    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.
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    Reflecting upon reflections
    (2009-06-01) Zeitler, H.; Camp, D.
    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