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Elementary Mathematics from a Higher Standpoint, Volume 2 - Geometry (Paperback, 2016 ed.)
Loot Price: R2,639
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Elementary Mathematics from a Higher Standpoint, Volume 2 - Geometry (Paperback, 2016 ed.)
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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.
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