id: 06592095
dt: b
an:
au: Klein, Felix
ti: Elementary mathematics from a higher standpoint. Volume II: Geometry.
Translated from the 4th German edition by Gert Schubring.
so: Berlin: Springer (ISBN 978-3-662-49443-1/pbk; 978-3-662-49445-5/ebook;
978-3-662-49515-5/set). xvi, 315~p. (2016).
py: 2016
pu: Berlin: Springer
la: EN
cc: G10
ut:
ci: Zbl 1341.11001; Zbl 1339.26002; JFM 51.0055.13
li: doi:10.1007/978-3-662-49445-5
ab: Publisher’s description: These three volumes constitute the first
complete English translation of Felix Klein’s seminal series
“Elementarmathematik vom höheren 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. For
Volumes I and III see [Zbl 1341.11001; Zbl 1339.26002]. See the review
of the 3rd German edition in [JFM 51.0055.13].
rv: