Geometry by Its Transformations

Lessons Centered on the History from 1800-1855

Häftad, Engelska, 2025

619 kr

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This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years.

Produktinformation

Utgivningsdatum2025-02-08
Mått155 x 235 x 13 mm
Vikt347 g
FormatHäftad
SpråkEngelska
SerieCompact Textbooks in Mathematics
Antal sidor205
FörlagBirkhauser Verlag AG
ISBN9783031722806

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Christopher Baltus has degrees in history (BA), mathematics education (MAT), and mathematics (PhD). After three years of secondary mathematics teaching and two years in the Peace Corps, he taught college mathematics for 36 years. His article “Poncelet’s discovery of homology” appeared in Historia Mathematica, May 2023. In retirement, in Poughkeepsie, NY, he and his wife volunteer in an elementary school, he as an in-the-classroom mathematics aide.

Introduction.- 1. Greek Background.- 2. The Dilation Transformation.- 3. Institutional Transformation of Geometry: France.- 4. Affinity and the List of Transformations by Moebius.- 5. Background for Homology: the Common Secant, the Cross-Ratio, and Harmonic Sets.- 6. Plane-to-Plane Projection.- 7. Homology as developed by La Hire and Poncelet.- 8. Matrices and Homogeneous Coordinates.- 9. Projective Geometry: Steiner and von Staudt.- 10. Transformation in German Universities.- 11. Geometric Inversion.- 12. Moebius Transformation.- 13. Topic after 1855: Beltrami-Klein Model.- 14. Topic after 1855: Isometries and Dilations in French Schoolbooks.