Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century

Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century

2011 | 424 | ISBN: 0857290592 | PDF | 3 Mb

Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plucker s equations) and their role in resolving a paradox in the theory of duality; to Riemann s work on differential geometry; and to Beltrami s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry rose to prominence, and looks at Poincare s ideas about non-Euclidean geometry and their physical and philosophical significance. ...