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Collineations and Conic Sections Christopher Baltus

Collineations and Conic Sections By Christopher Baltus

Collineations and Conic Sections by Christopher Baltus

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Summary

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.

Collineations and Conic Sections Summary

Collineations and Conic Sections: An Introduction to Projective Geometry in its History by Christopher Baltus

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.

Collineations and Conic Sections Reviews

The text is organised into fiffteen chapters and deals with a wealth of classical topics. The explicit exposition of all these topics is carried out in view of their history. The reader will find detailed information about Euclid's Elements and the treatment of conic sections by Greek mathematicians such as Apollonius of Perga and Archimedes. (Hans Havlicek, Mathematical Reviews, April, 2022)

This is a historically very well informed look at projective geometry, central collineations, and conics. The reader is exposed to both a wealth of results in projective geometry and to the motivations behind them . The author has rendered a genuine service to the reader interested in this topic, as there is no contemporary book one could turn to both learn the basic techniques of projective geometry and to find out about its historical intricacies. (Victor V. Pambuccian, zbMATH 1460.51001, 2021)

Table of Contents

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.

Additional information

NPB9783030462864
9783030462864
3030462862
Collineations and Conic Sections: An Introduction to Projective Geometry in its History by Christopher Baltus
Christopher Baltus
New
Hardback
Springer Nature Switzerland AG
2020-09-02
187
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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