Worlds out of nothing : a course in the history of geometry in the 19th century
Gray, Jeremy.
Worlds out of nothing : a course in the history of geometry in the 19th century - London ; Springer, 2011. - xxv, 384 p. : ill. ; 24 cm. - Springer undergraduate mathematics series 1615-2085 .
Includes bibliographical references (p. 359-376) and index.
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.
9780857290595
Geometry--History--19th century.
Euclid
Differential geometry
Geometrie--evolution
History of mathematics
Projective geometry
514 / GRA-W
Worlds out of nothing : a course in the history of geometry in the 19th century - London ; Springer, 2011. - xxv, 384 p. : ill. ; 24 cm. - Springer undergraduate mathematics series 1615-2085 .
Includes bibliographical references (p. 359-376) and index.
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.
9780857290595
Geometry--History--19th century.
Euclid
Differential geometry
Geometrie--evolution
History of mathematics
Projective geometry
514 / GRA-W
