Basic optimisation methods

education while providing scope for imaginative design and investigational initiatives. I can see many children and adults being hooked, and filling up discs with records of their designs and 'discoveries'. With a seven colour display, the user is initially given the option of setting up a square frame which can then be stretched at will into a rectangle or parallelogram, and/or rotated, to whatever extent is desired. The user may then (or previously) change the shape and colour of the sides of this basic tile while keeping the corners fixed and/or draw within it in seven colours, automatically invoking a range of symmetry options. For instance, if designing inside a square, you are presented with options of no symmetry, half turn symmetry, reflection in mediators of sides or diagonals, glide reflection or rotational symmetry of order 4. If you choose the last of these, for instance, any design you draw is automatically copied so that the final result has symmetry of order 4. Mistakes can easily be erased and the completed design can then be tessellated automatically to a chosen scale. With the aid of the library disc supplied, the seventeen wallpaper-pattern symmetry groups may be investigated. Patterns can be printed out in colour or black and white (depending of course on your printer!). The whole program is extraordinarily easy to operate and for nearly all purposes, involves the use of the space bar, return key and arrow keys only. Overall I feel very enthusiastic about the possibilities of this package and think it likely to be in demand, as the basis of various projects at my own school, by children of widely differing age, ability and experience.