Braunschweig & Berlin, Germany: Friedr. Vieweg & Sohn/Julius Springer, 1922, 1923, 1924. First Edition.  pp. 8vo. Marbled paper covered boards with gold embossed title on green leather patch affixed to front board. Clean within. Title pages for each extract also bound in.
In 1922, Russian mathematician Alexander Alexandrovich Friedmann [or Friedman] (1888-1925) developed solutions to Einstein’s general relativity field equations under the simplifying (but realistic) assumption that the universe is “homogeneous and isotropic,” meaning that at large scales, the universe looks the same from every location (homogeneous) and in every direction (isotropic). Friedmann found that his solutions depended on just two parameters: Omega, the average density of matter and energy in the universe, and Lambda, the vacuum energy associated with empty space (the cosmological constant). By varying these parameters, Friedmann was able to create models of the universe that expanded, collapsed or was stable. These papers include (1) Friedmann's three solutions; (2-3) Two notes from Einstein, first doubting the result and then conceding its correctness; (4) A further paper by Friedmann on the topic of the curvature of space. The articles are as follows: “Über die Krümmung des Raumes” (“On the Curvature of Space”) by Alexander Friedmann (Zeitschrift für Physik 10, pp. 377–386, 1922); and “Bemerkung zu der Arbeit von A. Friedmann ‘Über die Krümmung des Raumes’” (“Comment on the work of A. Friedmann ‘On the curvature of space’”) by Albert Einstein (Zeitschrift für Physik 11 p. 326, 1922); and “Notiz du der Arbeit von A. Friedmann ‘Über die Krümmung des Raumes’” (“Your note on the work of A. Friedmann “On the Curvature of Space’”) by Albert Einstein (Zeitschrift für Physik 16 No. 3 p. 228, 1923); and “Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes” (“On the possibility of a world with constant negative curvature of space”) by Alexander Friedmann (Zeitschrift für Physik 21 pp. 326–332, 1924).