Collineations and Conic Sections
An Introduction to Projective Geometry in its History
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Beschreibung
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
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
Gives the necessary geometry to readers of limited background Provides reader with a general history through the mid-nineteenth century Features a proof-based treatment
Autor*in
Christopher Baltus
Themen in »Collineations and Conic Sections«
Desargues’ theorem Euclid's Elements ancient Greek mathematics group properties conics Apollonius harmonic division Philippe de la Hire Jean-Victor Poncelet involution foci matrices for collineations
Stimmen zu »Collineations and Conic Sections«
“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)
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