Geometry by Its Transformations Lessons Centered on the History from 1800-1855 /
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. The book starts with the background needed from Euclid’s Elements, followed by chapters on transformations, including dilation (similit...
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| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham :
Springer Nature Switzerland : Imprint: Birkhäuser,
2025.
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| Ausgabe: | 1st ed. 2025. |
| Schriftenreihe: | Compact Textbooks in Mathematics,
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| Online-Zugang: | https://doi.org/10.1007/978-3-031-72281-3 |
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Inhaltsangabe:
- 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.