The relationship between geometry and geodesy from the historical point of view. (Das Verhältnis von Geometrie und Geodäsie aus historischer Sicht.) (German) Zbl 0717.01001

The most outstanding achievements using the links between geometry and geodesy are listed from Eratosthenes earthmeasuring till geometrical methods in cosmical geodesy. The famous books on differential geometry of surfaces by L. Bianchi (1886) and G. Darboux (1887-) and F. Helmert’s work “Die mathematischen und physikalischen Theorien der höheren Geodäsie” (two volumes, Leipzig, 1880 und 1884) show that a century ago these two disciplines were very near to each other. Later they developed in different directions and only from the 1950s onwards a new approach can be considered. The vector and tensor calculus were introduced in geodesy in the books of C. F. Baeschlin [Lehrbuch der Geodäsie. Zürich: Orell Füssli Verlag (1948; Zbl 0040.38701)] and M. Hotine [Mathematical geodesy. Washington, D.C.: U.S. Department of Commerce (1969; Zbl 0197.50805)], respectively. In 1980 a research group “Differential geometry of the gravity field” was organized by the International Association of Geodesy, now even the Cartan method of exterior differential forms is used in geodesy.
Reviewer: Ü.Lumiste


01A05 General histories, source books
86A30 Geodesy, mapping problems
58A15 Exterior differential systems (Cartan theory)