New standards for the solution of geometric calculation problems by using computers

The availability of computers and of software for the geometric tasks of construction, measurement and calculation, as well as the availability of software for numerical and symbolic computation induce new methods for the solution of geometric calculation problems: computer-aided graphical, numerical and algebraic methods of solution. These computer-aided solutions are explained in relation to suitably chosen tools (Mathematica and Cabri Géomètre) and traditional examples.     

A dynamic approach to ‘simple’ algebraic curves

Despite its low relevance for teaching in schools the desideratum “Algebraic Curves’ has always been an issue within mathematical didactics. This article aims to continue this tradition with respect to a project oriented mathematics instruction by applying current dynamic geometry software (Cabri II+).     

An improved typology of cutting and packing problems

The number of publications in the area of Cutting and Packing (C&P) has increased considerably over the last two decades. The typology of C&P problems introduced by Dyckhoff [Dyckhoff, H., 1990. A typology of cutting and packing problems. European Journal of Operational Research 44, 145–159] initially provided an excellent instrument for the organisation and categorisation of existing and new literature. However, over the years also some deficiencies of this typology became evident, which created problems in dealing with recent developments and prevented it from being accepted more generally. In this paper, the authors present an improved typology, which is partially based on Dyckhoff’s original ideas, but introduces new categorisation criteria, which define problem categories different from those of Dyckhoff. Furthermore, a new, consistent system of names is suggested for these problem categories. Finally, the practicability of the new scheme is demonstrated by using it as a basis for a categorisation of the C&P literature from the years between 1995 and 2004.