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Geometry II - Spaces of Constant Curvature (Paperback, Softcover reprint of the original 1st ed. 1993)
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Geometry II - Spaces of Constant Curvature (Paperback, Softcover reprint of the original 1st ed. 1993)
Series: Encyclopaedia of Mathematical Sciences, 29
Expected to ship within 18 - 22 working days
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Spaces of constant curvature, i.e. Euclidean space, the sphere, and
Loba chevskij space, occupy a special place in geometry. They are
most accessible to our geometric intuition, making it possible to
develop elementary geometry in a way very similar to that used to
create the geometry we learned at school. However, since its basic
notions can be interpreted in different ways, this geometry can be
applied to objects other than the conventional physical space, the
original source of our geometric intuition. Euclidean geometry has
for a long time been deeply rooted in the human mind. The same is
true of spherical geometry, since a sphere can naturally be
embedded into a Euclidean space. Lobachevskij geometry, which in
the first fifty years after its discovery had been regarded only as
a logically feasible by-product appearing in the investigation of
the foundations of geometry, has even now, despite the fact that it
has found its use in numerous applications, preserved a kind of
exotic and even romantic element. This may probably be explained by
the permanent cultural and historical impact which the proof of the
independence of the Fifth Postulate had on human thought."
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