02766nam 22004335a 450 991015361490332120101201234500.03-03719-587-810.4171/087(CKB)3710000000962492(CH-001817-3)123-101201(PPN)178155853(EXLCZ)99371000000096249220101201j20101201 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierNikolai I. Lobachevsky, Pangeometry[electronic resource] /Athanase PapadopoulosZuerich, Switzerland European Mathematical Society Publishing House20101 online resource (322 pages)Heritage of European Mathematics (HEM) ;2523-5214Lobachevsky wrote his Pangeometry in 1855, the year before his death. This memoir is a résumé of his work on non-Euclidean geometry and its applications, and it can be considered as his clearest account on the subject. It is also the conclusion of his lifework, and the last attempt he made to acquire recognition. The treatise contains basic ideas of hyperbolic geometry, including the trigonometric formulae, the techniques of computation of arc length, of area and of volume, with concrete examples. It also deals with the applications of hyperbolic geometry to the computation of new definite integrals. The techniques are different from those found in most modern books on hyperbolic geometry since they do not use models. Besides its historical importance, Lobachevsky's Pangeometry is a beautiful work, written in a simple and condensed style. The material that it contains is still very alive, and reading this book will be most useful for researchers and for students in geometry and in the history of science. It can be used as a textbook, as a source book and as a repository of inspiration. The present edition provides the first complete English translation of the Pangeometry that appears in print. It contains facsimiles of both the Russian and the French original versions. The translation is accompanied by notes, followed by a biography of Lobachevky and an extensive commentary.History of mathematicsbicsscHistory and biographymscGeometrymscDifferential geometrymscHistory of mathematicsHistory and biographyGeometryDifferential geometry01-xx51-xx53-xxmscPapadopoulos Athanase59547ch0018173BOOK9910153614903321Nikolai I. Lobachevsky, Pangeometry2564448UNINA