TY  - BOOK
AU  - Gray,Jeremy
TI  - Worlds out of nothing: a course in the history of geometry in the 19th century
T2  - Springer undergraduate mathematics series
SN  - 9780857290595
U1  - 514 
PY  - 2011///
CY  - London
PB  - Springer
KW  - Geometry
KW  - History
KW  - 19th century
KW  - Euclid
KW  - Differential geometry
KW  - Geometrie
KW  - evolution
KW  - History of mathematics
KW  - Projective geometry
N1  - Includes bibliographical references (p. 359-376) and index
N2  - 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 (Plücker’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 Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance.

Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for
UR  - https://link.springer.com/book/10.1007/978-0-85729-060-1#toc
UR  - https://www.goodreads.com/book/show/1262860.Worlds_Out_of_Nothing?from_search=true&from_srp=true&qid=VStq2U0ZDZ&rank=1#CommunityReviews
UR  - https://link.springer.com/book/10.1007/978-0-85729-060-1
ER  -