This chapter examines the design of digital technologies and associated forms of
learning activities for a range of geometries. The purpose is analyzing how design is
influenced by the mathematics involved, by the affordances (and constraints) of the
available technology, and by the needs of the learner. If space had permitted an even
longer chapter title, then the borrowing of Abbott’s (1884) subtitle a romance of many
dimensions could well be appropriate. While there is no space in this particular chapter
for analyses focusing on other areas of mathematics (such as algebra or statistics),
such analyses would usefully complement this chapter and are to be encouraged.