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Collineations and Conic Sections An Introduction to Projective Geometry in its History




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 09/2021
Edizione: 1st ed. 2020





Trama

This volume combines an introduction to central collineations with an introduction to projective geometry, set in its historical context and aiming to provide the reader with a general history through the middle of the nineteenth century. Topics covered include but are not limited to:
  • The Projective Plane and Central Collineations
  • The Geometry of Euclid's Elements
  • Conic Sections in Early Modern Europe
  • Applications of Conics in History
With rare exception, the only prior knowledge required is a background in high school geometry. As a proof-based treatment, this monograph will be of interest to those who enjoy logical thinking, and could also be used in a geometry course that emphasizes projective geometry.




Sommario

Preface.- 1. Introduction.- 2. Central Collineations.- 3. The Geometry of Euclid's Elements.- 4. Conics in Greek Geometry.- 5. Conic Sections in Early Modern Europe.- 6. Conic Sections in Early Modern Europe.- 7. Central Collineations.- 8. Nineteenth Century.- 9. Foci.- 10. Steiner. 11. Desargues and Involution.- 12. Looking Ahead.- 13. Matrices and Homogeneous Coordinates.- 14. Some Applications of Conics in History.- 15. Vertical Stretch and Isaac Newton's Conics.- 16. Three Appendices.- Bibliography.










Altre Informazioni

ISBN:

9783030462895

Condizione: Nuovo
Dimensioni: 235 x 155 mm
Formato: Brossura
Illustration Notes:XI, 187 p.
Pagine Arabe: 187
Pagine Romane: xi


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