Extra reading  
If you have enjoyed this small introduction to taxicab geometry, and would like to know more about this subject and/or about computational geometry and pattern recognition in general, this is a short list of references. I highly recommend the taxicab geometry page from GVSU and the book by Krause. (And of course the projects of my fellow students!)
Computational geometry and pattern recognition are widely documented on the web, but I think these are a good place to start.

Computational Geometry course

Pattern Recognition course

student projects in both courses

Taxicab Geometry (Astudent project from GVSU)

Voronoi diagrams and friends (Another student project, from Carleton College)

Voroglide (featuring a very good applet)

Practice your french with the french version of this page.

[1] Eugene F. Krause, Taxicab Geometry, Addison-Wesley, Menlo Park, 1975.

[2] Martin Gardner, "Mathematical Games", Scientific American, 243 (Nov. 1980), pp. 18-30.