Definition
Geodesy is the branch of mathematics concerned with the shape and area of the earth and with the location of points on it.
Cartography is the art, science, and practice of making maps.
A map projection, or simply a projection, is any systematic representation of the earth's surface onto another surface.
The Global Positioning System, or GPS, comprises a network of satellites that orbit the earth and, by radio communications with land-based receivers, enable the accurate determination of the coordinates of points on the earth's surface.
Spherical geometry is the study of lines, angles, and areas on a spherical surface.
Historical Background
The foundation of geographical information science (GIS) lies in our ability to determine the size and shape of the earth, locate points on its surface, measure its features, and to portray the earth in maps. Thus, geodesy and cartography form the basis of GIS. In turn, both of these subjects are built on strong...
Recommended Reading
Banerjee, S.: Revisiting Spherical Trigonometry with Orthoginal Projectors, College Math. J. 35(5), 375–381 (2004)
Berggren, J.L., Jones A.: Ptolemy's Geography. Princeton University Press, Princeton (2000)
Bosowski, E.F., Feeman T.G.: The use of scale factors in map analysis: an elementary approach. Cartographica 34(4), 35–44 (1997)
Bugayevskiy, L.M., Snyder J.P.: Map Projections: AÂ Reference Manual. Taylor and Francis, London (1995)
Cotter, C.H.: The Astronomical and Mathematical Foundations of Geography. American Elsevier, New York (1966)
Dent, B.D.: Cartography, 4th edn. Wm. C. Brown, Dubuque (1996)
Espenshade, E.B. Jr., et al. (eds.): Goode's World Atlas. 19th edn. Rand McNally, Skokie, Illinois, USA (1995)
Feeman, T.G.: Portraits of the Earth: AÂ Mathematician Looks at Maps. American Mathematical Society, Providence (2002)
Forman S, Steen L (2006) Global Positioning System. http://www.stolaf.edu/other/ate/gps.html. Accessed 8 May 2006
Nord, G., Jabon, D., Nord J.: The Global Positioning System and the Implicit Function Theorem. SIAM Rev. 40(3), 692–696 (1998)
Snyder, J.P.: Flattening the Earth: Two Thousand Years of Map Projections. University of Chicago Press, Chicago (1993)
Thompson, R.B.: Global Positioning System: The Mathematics of GPS Receivers. Math. Magazine 71(4), 260–269 (1998)
Wikipedia (2006) Global Positioning System. http://en.wikipedia.org. Accessed 8 May 2006
Wikipedia (2006) Trilateration. http://en.wikipedia.org. Accessed 8 May 2006
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
Feeman, T. (2008). Mathematical Foundations of GIS. In: Shekhar, S., Xiong, H. (eds) Encyclopedia of GIS. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35973-1_761
Download citation
DOI: https://doi.org/10.1007/978-0-387-35973-1_761
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-30858-6
Online ISBN: 978-0-387-35973-1
eBook Packages: Computer ScienceReference Module Computer Science and Engineering