Geometry meets the computer

In a rather short space of time, computers have changed in character from being large numerical devices that could only be communicated with obliquely to small visual devices that allow for much more direct forms of person-machine communication. We have gone from the roomfull to the pocketfull, from paper tape and punched cards to keyboards, mice and touch screens and from strings of binary digits to visual images. All of this has taken not much more than one (human) generation. The IBM Corporation confidently predicted in 1945 that there would never be a market for more than two or three computers in the world, and yet in affluent countries like Australia, there are already many households with more computers than that, depending a bit on how one defines 'computer'.