Chaotic Properties of Single Element Nonlinear Chimney Model: Effect of Directionality

We generalize the chimney model by introducing nonlinear restoring and gravitational forces for the purpose of modeling swaying of trees at high wind speeds. We have derived the general equations governing the system using Lagrangian formulation. We studied the simplest case of a single element in more detail. The governing equation we arrive at for this case has not been studied so far. We study the chaotic properties of this simple building block and also the effect of directionality in the wind on the chaotic properties. We also consider the special case of two elements.

Template-promoted self-replication in dynamic combinatorial libraries made from a simple building block

Self-assembly driven self-replication based on a very simple building block is facilitated by a template.

Building understanding: Sensitive issues and putting the researcher in the research

Stemming from ethnographic research in a chronically poor district of rural Uganda, this paper recounts a number of attempts to investigate young people’s understanding of HIV and its transmission. The failure of the initial, more traditional methodologies are used to critically evaluate the positionality or role the researcher played as she became embedded within the community to the extent she lost objectivity as a researcher. Inadvertently, a simple building block game was used as a methodology. This was successful in generating interesting ‘data’ and proved that even research groups deemed difficult to access can be reached with some methodological consideration. The tool was, however, almost over successful and generated dramatic ethical dilemmas which ethically questioned the potential of the research and had a significant impact on the researcher. This paper therefore stresses the necessity to give ethical consideration to the research and its participants but to not over look the researcher.

Activities for Students: Inquiry into Fractals

The exotic images of fractals often pique the interest of high school mathematics students, and this interest presents an opportunity for geometry teachers to draw students into an investigation of transformations and patterns. By using a simple building block and fractals' self-imaging characteristic (as the figure grows, it retains the pattern established by the building block), teachers can bring construction of fractals into the high school geometry curriculum. The three activities described in this article engage students in constructing a fractal, searching a fractal for patterns, and using transformations to build different fractals. Students gain insight into patterns as their fractals grow; they flip or rotate fractal pieces by following a design and translating the pieces into place.