Gaussian land survey
The Gaußsche Landesaufnahme (1827 to 1861) was created as a continuation of the Kurhannoverschen Landesaufnahme by order of the Royal Ministry of the Interior in what was then the Kingdom of Hanover .
history
The state survey was preceded by the triangulation of the Kingdom of Hanover by the mathematician Carl Friedrich Gauß . This took place in the years 1821 to 1825 and was the basis for the surveying work of the land survey. It was picked up by young officers of the General Staff and the Engineering and Artillery Corps in the years 1827 to 1861. To carry out this work, a measuring table and tilting rule were used.
The state record was limited to those areas that came to Hanover after the Congress of Vienna in 1815 . These were the Lower County of Lingen , the Duchy of Arenberg-Meppen , the County of Bentheim , the Hildesheim Monastery , the city of Goslar and areas of the Lower Field . The map series is therefore also referred to as the Gaussian land survey of the areas acquired by Hanover in 1815 .
The map series comprised 61 sheets, these represented an area of 7,000 × 7,000 meters on a scale of 1: 21,333⅓, they were monochrome (the copy of the First Crafts School Berlin, the later Gauß State Engineering Academy , today preserved in the Berlin State Library , was in 5 Colored colors, as well as the template for the full-format facsimile edition) and had a square format of around 33 × 33 centimeters.
Today, scaled-down reproductions to the round scale 1: 25,000, which were put together to form large sheets, are available from the State Office for Geoinformation and Land Surveying Lower Saxony (LGN).
Triangle Hoher Hagen - Brocken - Großer Inselsberg
As part of the national survey of the Kingdom of Hanover carried out by Carl Friedrich Gauß between 1818 and 1826 by triangulation , Gauß also measured his "large triangle" Hoher Hagen - Brocken - Großer Inselsberg . This triangle with side lengths of 69 km (Hoher Hagen - Brocken), 84 km (Hoher Hagen - Inselsberg) and 106 km (Brocken - Inselsberg) was the basis for linking numerous regional survey data.
Since Gauss already considered non-Euclidean geometry to be possible at that time and he knew that the axiom of parallels was dispensable, the legend developed about the measurement of the large triangle that Gauss had empirically on the occasion of the Hanoverian land survey after a deviation of the sum of angles from the Euclidean triangle Looking for a value of 180 °, as in this triangle formed by the Hohen Hagen, the Brocken and the Inselberg. The measurement by Gauss is proven. The above-mentioned assumption about motivation, on the other hand, is uncertain. Max Jammer wrote about the result of this Gaussian measurement:
"It hardly needs to be specifically stated that he did not discover any deviation of 180 ° within the error limit and from this he drew the conclusion that the structure of real space is, as far as experience allows a statement, Euclidean."
See also
Web links
Individual evidence
- ↑ A comprehensive description of this famous Gaussian measurement can be found, for example, in Charles Kittel et al .: Berkeley Physik . Course 1: Mechanics , 5th, improved edition, Braunschweig / Wiesbaden, 1991. Walter D. Knight: Mechanics. Springer, Berlin / Heidelberg 2001, ISBN 978-3-540-41569-5 , p. 5. Restricted preview in the Google book search
- ↑ Erhard Scholz thinks it is quite possible that Gauss thought of it; arxiv : math.HO / 0409578 . Gauss himself expresses himself in a letter to Olbers dated March 1, 1827, quoted by Walter Kaufmann-Bühler: Gauß - a biographical study . Springer-Verlag, 1987, p. 97. to the effect that the measurement errors are too large for such a determination of deviations.
- ↑ Max Jammer: The problem of space. Darmstadt 1960, p. 164.