[FOM] Gauss and non-Euclidean geometry

[josef@us.es]

Dear colleagues,

On this topic, I'd like to mention that the best study today is by Erhard Scholz, who has analyzed very carefully the matter of 
Gauss's observational determination of a big geodesic triangle. See his “C. F. Gauss’ Prazisionsmessungen terrestrischer 
Dreiecke und seine Uberlegungen zur empirischen Fundierung der Geometrie in den 1820er Jahren”, in Form, Zahl, Ordnung. 
Studien zur Wissenschaftsgeschichte. Festschrift fur Ivo Schneider zum 65. Geburtstag, R. Seising, M. Folkerts, U. Hashagen 
eds. (Stuttgart, Steiner, 2004), pp. 355–380. You can also access the paper in Spanish here:

divulgamat.ehu.es/weborriak/ Historia/Gaceta/historia83.pdf

Contrary to what many say, the story seems to be right, Gauss did measure the big trianle of the peaks Hohenhagen, 
Inselsberg, Brocken, although not solely for an empirical determination of the right geometry of space (rather, he took 
advantage of the fact that, anyway, he needed to make geodesic measurements for professional reasons). The exactness of his 
meaurements is quite amazing, according to experts in the matter. On the other hand, although Gauss knew that astronomical 
measurements would be much more relenvant, it happens that he was aware of sources of experimental error that made them 
quite useless in his time (a point of which Lobatchevskii was unaware), and this is one reason why he opted for terrestrial 
measures.

Best,

Jose Ferreiros