Elementary Mathematics from a Higher Standpoint: Volume II: Geometry

by Felix Klein, Gert Schubring (Translator)

These three volumes constitute the first complete English translation of Felix Klein s seminal series Elementarmathematik vom hoheren Standpunkte aus . Complete has a twofold meaning here: First, there now exists a translation of volume III into English, while until today the only translation had been into Chinese. Second, the English versions of volume I and II had omitted several, even extended parts of the original, while we now present a complete revised translation into modern English.
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."

Genres: Mathematics, Textbooks

331 pages, Paperback

First published January 1, 1925

Reviews

[Eric · Rating 5 out of 5]

I have the (copyright) 1939 Dover edition of this work.