In this chapter we have shown how key decisions taken by designers of digital
technologies for mathematics are influenced both by the mathematics involved (in
the case of this chapter by geometrical ideas of projection, curvature, local and
global co-ordinates, and so on), and by the affordances of the available flat-screen
technology. For more examples of the design process see Battista (2008), where a
case study of the design of a 2D geometry microworld is presented, and Christou
et al. (2006), where the theoretical considerations in the design of a form of 3D
geometry software are revealed.