Overview
- New translation of the classic volume on geometry
- Invaluable treatise for any mathematics educator
- Exhibits the connections between geometry and more formalistic mathematics
- Includes supplementary material: sn.pub/extras
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Table of contents (17 chapters)
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The Simplest Geometric Formations
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Geometric Transformations
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Systematic Discussion of Geometry and its Foundations
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Observations About the Teaching of Geometry
Keywords
About this book
The volumes, first published between 1902 and 1908, are lecture notes of courses that Klein offered to future mathematics teachers, realizing a new form of teacher training that remained valid and effective until today: Klein leads the students to gain a more comprehensive and methodological point of view on school mathematics. The volumes enable us to understand Klein’s far-reaching conception of elementarisation, of the “elementary from a higher standpoint”, in its implementation for school mathematics.
This volume II presents a paradigmatic realisation of Klein’s approach of elementarisation for teacher education. It is shown how the various geometries, elaborated particularly since the beginning of the 19th century, are revealed as becoming unified in a new restructured geometry. As Klein liked to stress: “Projective geometry is all geometry”. Non-Euclidean geometry proves to constitute a part of this unifying process. The teaching of geometry is discussed in a separate chapter, which provides moreover important information on the history of geometry teaching and an international comparison.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Elementary Mathematics from a Higher Standpoint
Book Subtitle: Volume II: Geometry
Authors: Felix Klein
Translated by: Gert Schubring
DOI: https://doi.org/10.1007/978-3-662-49445-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Education, Education (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2016
Softcover ISBN: 978-3-662-49443-1Published: 06 July 2016
eBook ISBN: 978-3-662-49445-5Published: 29 June 2016
Edition Number: 1
Number of Pages: XVI, 315
Number of Illustrations: 157 b/w illustrations
Additional Information: Original German edition published by Verlag Julius Springer, Berlin, Germany, 1925