"Conformal Mappings", by Steven G. Krantz. American Scientist,September/October 1999, pages 436-445.
Just as there are many ways to create two-dimensional maps of the earth, thereare many ways to create maps of objects scientists want to study, such as thehuman brain. Mathematics provides many kinds of maps suitable for differentpurposes. Conformal maps, like the well known Mercator projection incartography, have two main virtues: they expand or contract distances evenly inall directions, and they preserve angles. And like the Mercator projection,conformal maps have limitations: For example, they greatly distort areas. But,as Krantz puts it, "Any flat map of a curved space must sacrifice something."He goes on to explain, in a highly understandable and engaging fashion, thequite sophisticated mathematics of conformal maps. The article also discusses"quasiconformal" maps, which provide practical approximations to conformalmaps and are used in a wide variety of scientific applications, one examplebeing brain research.
--- Allyn Jackson