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Geometry by its transformations = lessons centered on the history from 1800-1855 /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Geometry by its transformations/ by Christopher Baltus.
其他題名:	lessons centered on the history from 1800-1855 /
作者:	Baltus, Christopher.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xviii, 205 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Geometry. -
電子資源:	https://doi.org/10.1007/978-3-031-72281-3
ISBN:	9783031722813

Geometry by its transformations = lessons centered on the history from 1800-1855 /
Baltus, Christopher.

Geometry by its transformationslessons centered on the history from 1800-1855 /[electronic resource] :by Christopher Baltus. - Cham :Springer Nature Switzerland :2025. - xviii, 205 p. :ill. (some col.), digital ;24 cm. - Compact textbooks in mathematics,2296-455X. - Compact textbooks in mathematics..

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.

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 (similitude), homology, homogeneous coordinates, projective geometry, inversion, the Möbius transformation, and transformation geometry as in French schoolbooks of 1910. Projective geometry is presented by tracing its path through the work of J. V. Poncelet, J. Steiner, and K. G. C. von Staudt. Extensive exercises are included, many from the period studied. The prerequisites for approaching this course are knowledge of high school geometry and enthusiasm for mathematical demonstration. This textbook is ideal for a college geometry course, for self-study, or as preparation for the study of modern geometry.

ISBN: 9783031722813

Standard No.: 10.1007/978-3-031-72281-3doiSubjects--Topical Terms:

579899
Geometry.

LC Class. No.: QA443.5

Dewey Class. No.: 516.009

Geometry by its transformations = lessons centered on the history from 1800-1855 /
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