When you don't know where you're going, any route is as good as another. Knowing where you are isn't as important as being able to find your way back later. Mankind has been crawling over this planet on land and sea for millennia and, as you would expect, finding our way gets easier each day. This month we dive into the morass we call the Web in search of zero-cost, non-commercial, registration-free resources aimed at providing you with practical information about global positioning systems (GPS) and geographical information systems (GIS).
Spherical geometry and trig
Technically speaking, of course, there's really no way that a flat map or monitor screen can display an accurate image of the earth's surface. But, let's just assume for the moment that the enormous size of this ball of dirt flying through space and the relatively tiny surface area a typical map or chart depicts will allow us to circumvent the annoying immutable mathematical truth.
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When one starts navigating over distances that are significant fractions of the size of the earth, the technicalities can get a navigator lost, big time. In 1569, Gerardus Mercator introduced a new map projection for which he is best remembered. His maps showed longitude, latitude and rhomb lines as straight lines, a neat trick, considering the earth is round. He also introduced the term atlas to describe a collection of maps. But I digress.
The Euclidean theorems and axioms of plane geometry and trigonometry simply won't work on the surface of a ball. That's why we had to invent spherical versions of the same disciplines, using modified theorems and axioms that are obviously more complex than their planar cousins. That's why Vik Dhillon, Lecturer in Astrophysics in the Dept. of Physics and Astronomy at the University of Sheffield in the UK posted Spherical Geometry at http://www.shef.ac.uk/uni/academic/N-Q/phys/people/vdhillon/teaching/phy105/phy105_sphergeom.html to give a quick explanation of the workings of spherical math.
A more comprehensive explanation is found at http://math.rice.edu/~pcmi/sphere/, where the math department at Rice University posted its tutorial, The Geometry of the Sphere. It goes in more detail, that's certain, but the interactive graphics describing Girard's Theorem are worth your time and mouse muscles.
The topic has its own lingo and acronyms that may confuse the uninitiated. My advice is to push back the frontiers of ignorance and read Welcome to the GIS Dictionary, posted by the Association for Geographic Information and the University of Edinburgh's Department of Geography. The document contains nearly 1,000 terms, many of which apply to computers in general. Buried among the information on the site are more than 50 explanatory diagrams.
Go to http://www.geo.ed.ac.uk/agidict/welcome.html for a good word or two.
How GIS works
This is the digital age, after all, and not too many people want to handle the amount of paper needed to gather data for a geography-based project. Just think about what's involved in trying to site a new plant. Logistics is concerned with proximity to railroads and interstate highways. Finance is concerned with the state and county taxes. Production is concerned with a ready supply of suitable workers. Your architect would probably be interested in knowing the flatness of the terrain.
My guess is that few of us have sufficient resources and time to gather and correlate the information from dozens of maps into a site-specific master document that addresses every concern, let alone doing it for several candidate sites.
Geographic information systems can simplify the task. The secret is being able to overlay several precisely registered digital representations of those paper maps. To get the rudiments of how the technology functions, read Why is GIS Important to YOU? by the Vermont Center for Geographic Information, Inc. Point your mousie to http://www.vcgi.org/commres/publications/2page_gis.pdf, where you'll find a two-page document.
With your interest now sufficiently piqued, you could turn to our hired hands in Reston, Va. Click over to http://erg.usgs.gov/isb/pubs/gis_poster/ to see where the U.S. Coast Guard has posted its 34-page illustrated treatise on the topic. If you think GIS is something relatively new on the scene, you might want to investigate the section called GIS Through History.