Collineations and Conic Sections

An Introduction to Projective Geometry in its History

Christopher Baltus (Autor)

Buch | Softcover

XI, 187 Seiten

2021 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-46289-5 (ISBN)

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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.

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.

"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)

Erscheinungsdatum	04.09.2021
Zusatzinfo	XI, 187 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	314 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Themenwelt	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
Schlagworte	ancient Greek mathematics • Apollonius • conics • Desargues' theorem • Desargues’ theorem • Euclid's elements • foci • group properties • harmonic division • Involution • Jean-Victor Poncelet • matrices for collineations • Philippe de la Hire
ISBN-10	3-030-46289-7 / 3030462897
ISBN-13	978-3-030-46289-5 / 9783030462895
Zustand	Neuware