The ultimate aim is that a final version could be given to mathematics students to help them visualise non-Euclidean geometry. The programming language LOGO with its Turtle Graphics facilities is well known in educational circles. The turtle is a small triangular pointer that appears on the display screen. Using the turtle to draw in this way provides an easy introduction to computing for young children, but LOGO is equally suitable for older students. The system under development at Cardiff is specifically designed for exploring non-Euclidean geometry.
Euclidean geometry is the kind taught in schools.
The distinguishing feature of non-Euclidean geometry is the behaviour of parallel lines. Non-Euclidean geometry is difficult to visualise, and this is what makes the LOGO approach valuable. Both the hyperbolic and elliptic universes may be modelled by unit discs, with the turtle moving around inside, obeying non-Euclidean laws. The results are very striking and unfamiliar. In any figure drawn with the hyperbolic turtle, boxes of the same size will appear to shrink as the turtle moves outwards.