Lobachevski Illuminated: Content, Methods, and Context of the Theory of Parallels
Because our modern understanding of his work derives from these reinterpretations, many of Lobachevski's most striking ideas have been forgotten. To recover them, I have produced an "illuminated" version of Lobachevski's most accessible work, Geometrische Untersuchungen zur Theorie der Parallellinien (Geometric Investigations on the Theory of Parallels), a book that he published in 1840. I have produced a new English version of this work, together with extensive mathematical, historical, and philosophical commentary. The commentary expands and explains Lobachevski's often cryptic statements and proofs, while linking the individual propositions of his treatise to the related work of his predecessors (including Gerolamo Saccheri, J.H. Lambert, and A.M. Legendre), his contemporaries (including J·nos Bolyai and Karl Friedrich Gauss), and his followers (including Eugenio Beltrami, Henri PoincarÈ, and David Hilbert). This dissertation supplies the contemporary reader with all of the tools necessary to unlock Lobachevski's rich, beautiful, but generally inaccessible world.
Advisor:Gregory St. George; Karel Stroethoff
School:The University of Montana
School Location:USA - Montana
Source Type:Master's Thesis
Date of Publication:07/12/2007