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Creating maps of the world in a two-dimensional format has been a major challenge since antiquity. Over hundreds of years cartographers have developed many coordinate systems, called projections, to map their data.
Developing map projections can require solving problems in an area of mathematics known as differential geometry. A useful history of map projections is available in Flattening the Earth - Two Thousand Years of Map Projections (The University of Chicago Press, 1993) by the late J.P.Snyder, a chemical engineer turned cartographer.
Maple user Prof. Ross Taylor, from Clarkson University, stumbled into the world of cartography almost by accident. Taylor, also a chemical engineer by background, is the author or co-author of a number of articles on the application of Maple in numerical and engineering computing, as well as on the Maple packages Newton (for solving systems of nonlinear equations) and BESIRK (for solving mixed systems of differential and algebraic equations).
While studying a book by John Oprea from Cleveland State University, Differential Geometry and its Applications (Prentice-Hall 1997, ISBN 0-13-340738-1), Taylor became interested in using techniques described in that book to map the shorelines of the world in Maple.
Shoreline data in longitude/latitude format is freely available from a number of sources (for example, http://www. ngdc.noaa.gov:80/mgg/shorelines/gshhs.html). "The reason I was reading Oprea's book in the first place was that it made very extensive use of Maple to teach differential geometry," said Taylor.
Taylor and Oprea chose Maple as the development tool because it is the only environment that allowed them to write routines that combined the required algebraic and numeric solvers in an intuitive programming language. "Because Maple comes with tools for coordinate transformations and their graphical visualization already built in, it was very easy to make many of the projections in Maple," said Taylor. "Even with the more complicated projections, it was straightforward to make some modest modifications inside the Maple library. That's why I am addicted to Maple. It is the tool I turn to first. I can usually do things a lot quicker with Maple than I could with other [technical computation] tools."
The completed code was turned into a Maple package by one of Taylor's students, Richard Baur. The result is a highly interactive, engaging application that allows students and cartographers to gain insight into the mathematics of projections, and provides tools for developing new projections.
You can see for yourself by going to the Maple Application Center at http://www. maplesoft. com/apps/ html/maps1.html where we have the whole application in HTML (so you can browse it if you're not a Maple user), as well as the Maple Worksheets and code, available for download.
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