Subject: Re: [HM] Gauss experiment on three mountain peaks
From: Abe Shenitzer (shenitze@pascal.math.yorku.ca)
Date: Fri Feb 18 2000 - 15:51:30 EST
Why an astronomical, rather than a terrestrial, triangle?
Let c be the constant curvature of a surface. Let A be the area of a
triangle on the surface. The angular excess of a triangle is the sum of
its angles minus \pi. We have:
angular excess = c . A
(see, e.g., John Stillwell. Mathematics and its History, p. 249)
Abe Shenitzer
On 18 Feb 2000, Herbert Prinz wrote:
>
> W.K. Buehler, in his "Gauss, A Biographical Study", Springer 1981
> briefly mentions the famous measurement of the triangle
> Hohenhagen-Inselberg-Brocken, which was a geodetical control
> measurement. He considers it a myth that Gauss wanted thereby to
> decide the question of the Euclidean nature of space.
>
> However, there is an interesting footnote on p.100: "It was,
> incidentally, Lobachevski, who first proposed to investigate a
> stellar triangle for an experimental resolution of the question."
>
> I have been trying in vain to find more about this. Would anybody
> have an idea what Lobachevski had in mind?
>
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