This is the definitive presentation of the history, development
and philosophical significance of non-Euclidean geometry as well as
of the rigorous foundations for it and for elementary Euclidean
geometry, essentially according to Hilbert. Appropriate for liberal
arts students, prospective high school teachers, math. majors, and
even bright high school students. The first eight chapters are
mostly accessible to any educated reader; the last two chapters and
the two appendices contain more advanced material, such as the
classification of motions, hyperbolic trigonometry, hyperbolic
constructions, classification of Hilbert planes and an introduction
to Riemannian geometry.
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