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"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, there are many ways to create maps of objects scientists want to study, such as the human brain. Mathematics provides many kinds of maps suitable for different purposes. Conformal maps, like the well known Mercator projection in cartography, have two main virtues: they expand or contract distances evenly in all 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, the quite sophisticated mathematics of conformal maps. The article also discusses "quasiconformal" maps, which provide practical approximations to conformal maps and are used in a wide variety of scientific applications, one example being brain research.
--- Allyn Jackson
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