PART I: Early geometry; Euclidean geometry and the parallel
postulate; Investigations by Islamic mathematicians. PART II:
Saccheri and his Western Predecessors; J H Lambert's work;
Legendre's work; Gauss' contribution; Trigonometry; the first new
geometries; the discoveries of Lobachevskii and Bolyai; Curves and
surfaces; Riemann on the foundations of geometry; Beltrami's ideas;
New models and old arguments; Resume. PART III: Non-Euclidean
mechanics; The
question of absolute space; Space, time and space-time; Paradoxes
of special relativity; Gravitation and non-Euclidean geometry;
Speculations; Some last thoughts.
Reviews of this edition
'a very readable book that is stimulating and thought provoking.'
New Scientist
From reviews of the first edition
`Jeremy Gray has provided a superb exposition which tells a good
story.' Mathematics Teaching
'This promises to become a classic text for those interested in
considering changing mathematical perceptions of space. Gray's book
is a pleasure to read.' Historia Mathematica
`An admirable exposition for well-educated laymen of the evolution
of geometrical thought from before Euclid to black holes.' American
Mathematical Monthly
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