Über die Krümmung des Raumes. + Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes. + (Einstein's two remarks to the first paper): Bemerkung ... + Notiz ... - [THE CURVATURE OF SPACE]

(Berlin, Julius Springer, 1922-24). 8vo. In: ""Zeitschrift für Physik"", Vol. 10 (pp. 377 ff.),Vol.11 (pp.326), vol.16 (pp.228), vol.21 (pp.326-332). The entire four volumes offered here. Contemporary half cloth bindings.

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Two landmark papers in the history of cosmology: All first editions. In 'Über die Krümmung des Raumes' Friedman derived the non-stationary solutions to Einstein's field equations. Einstein quickly responded in a short comment ('Bemerkung'), in which he expressed his suspicion of such a model of the Universe and apparently pointed out an error in Friedman's calculations. However, Friedman now wrote a letter to Einstein, in which he enclosed his full calculations. Shortly after this, Einstein submitted a short notice (Notiz), in which he admitted that he himself had performed a calculation error and that Friedman's solutions, which shed new light on the matter, were valid. Friedman's expanding universe model was corroborated by Edwin Hubble's red-shift observations in 1929. In 'Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes' Friedman derived the Friedman-equations and demonstrated that he had command of all three Friedman-models describing positive, zero and negative curvature respectively, nearly a decade before the independent discoveries of the same models by Lemaître, Robertson, and Walker.