Geometry by Its Transformations
Lessons Centered on the History from 1800-1855
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Beschreibung
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.
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.
Introduces the foundations of geometry with reference to the subject's history Contains exercises that help the delivery of the course Suitable also for students in the humanities
Autor*in
Christopher Baltus
Themen in »Geometry by Its Transformations«
Projective geometry Transformations Synthetic geometry Euclidean geometry History of geometry
Stimmen zu »Geometry by Its Transformations«
“A notable strength of the book lies in the wealth of exercises provided at the end of each chapter. Selected solutions appear at the end of the volume, making the text well suited for both structured coursework and independent study. … this book presents a rich collection of material that is difficult to find elsewhere in such an integrated form. It is highly recommended for anyone interested in synthetic geometry and its historical development.” (Antonín Slavík, zbMATH 1570.01001, 2026)
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