Worlds Out of Nothing : A Course in the History of Geometry in the 19th Century
Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students in mathematics but will also appeal to the reader with a general interest in the his...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
London :
Springer London
[20..].
Cham : Springer Nature |
| Ausgabe: | 1st ed. 2010. |
| Schriftenreihe: | Springer Undergraduate Mathematics Series
|
| Schlagworte: | |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmerkung: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Worlds out of nothing, a course in the history of geometry in the 19th century, Jeremy Gray, [2nd edition], London, New York, Springer, 2011, 1 vol. (xxv-384 p.), Springer undergraduate mathematics series, 978-0-85729-059-5 • Worlds Out of Nothing, Texte imprimé, 9780857290618 |
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| 100 | 1 | |a Gray, Jeremy John, |d 1947-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Worlds Out of Nothing : |b A Course in the History of Geometry in the 19th Century |c by Jeremy Gray. |
| 250 | |a 1st ed. 2010. | ||
| 260 | |a London : |b Springer London. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Springer Undergraduate Mathematics Series |x 2197-4144 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a Mathematics in the French Revolution Poncelet (and Pole and Polar) Theorems in Projective Geometry Poncelet s Traité Duality and the Duality Controversy Poncelet, Chasles, and the Early Years of Projective Geometry Euclidean Geometry, the Parallel Postulate, and the Work of Lambert and Legendre Gauss (Schweikart and Taurinus) and Gauss s Differential Geometry János Bolyai Lobachevskii Publication and Non-Reception up to 1855 On Writing the History of Geometry 1 Across the Rhine Mo bius s Algebraic Version of Projective Geometry Plücker, Hesse, Higher Plane Curves, and the Resolution of the Duality Paradox The Plücker Formulae The Mathematical Theory of Plane Curves Complex Curves Riemann: Geometry and Physics Differential Geometry of Surfaces Beltrami, Klein, and the Acceptance of Non-Euclidean Geometry On Writing the History of Geometry 2 Projective Geometry as the Fundamental Geometry Hilbert and his Grundlagen der Geometrie The Foundations of Projective Geometry in Italy Henri Poincaré and the Disc Model of non-Euclidean Geometry Is the Geometry of Space Euclidean or Non-Euclidean? Summary: Geometry to 1900 What is Geometry? The Formal Side What is Geometry? The Physical Side What is Geometry? Is it True? Why is it Important? On Writing the History of Geometry 3 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students in mathematics but will also appeal to the reader with a general interest in the history of mathematics. Emphasis is placed on understanding the historical significance of the new mathematics: Why was it done? How - if at all - was it appreciated? What new questions did it generate? 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, as exemplified by Klein s Erlangen Program, rose to prominence, and looks at Poincaré s ideas about non-Euclidean geometry and their physical and philosophical significance. It then concludes with discussions on geometry and formalism, examining the Italian contribution and Hilbert s Foundations of Geometry; geometry and physics, with a look at some of Einstein s ideas; and geometry and truth. 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 | ||
| 650 | |a Géométrie |y XIXe siècle 1801 1900 | ||
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| 776 | 0 | |t Worlds Out of Nothing |b Texte imprimé |z 9780857290618 | |
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