Gauss-Krüger coordinate system

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In cartography, the term Gauss-Krüger, named after Carl Friedrich Gauss and Johann Heinrich Louis Krüger, is used in three slightly different ways.

• Often, it is just a synonym for the Transverse Mercator map projection. Another synonym is Gauss conformal projection.
• Sometimes, the term is used for a particular computational method for Transverse Mercator: that is, how to convert between latitude/longitude and projected coordinates. There is no simple closed formula to do so when the earth is modelled as an ellipsoid. But the Gauss-Krüger method gives the same results as other methods, at least if you are sufficiently near the central meridian: less than 10 degrees of longitude, say. Farther away, some methods become inaccurate.
• The term is also used for a particular set of Transverse Mercator projections used in narrow zones in Europe, at least in Germany, Austria, and Finland. This Gauss-Krüger system is similar to the Universal Transverse Mercator system, but the central meridians of the Gauss-Krüger zones are only 3° apart, as opposed to 6° in UTM. As a consequence, the scale variation within a Gauss-Krüger zone is about 1/4 of what it is in a UTM zone. More information on this system can be found on the German Wikipedia.