Download e-book for iPad: Geometry from a Differentiable Viewpoint by John McCleary

By John McCleary

ISBN-10: 0521116074

ISBN-13: 9780521116077

ISBN-10: 0521133114

ISBN-13: 9780521133111

the advance of geometry from Euclid to Euler to Lobachevsky, Bolyai, Gauss and Riemann is a narrative that's usually damaged into elements – axiomatic geometry, non-Euclidean geometry and differential geometry. This poses an issue for undergraduates: Which half is geometry? what's the vast photo to which those components belong? during this creation to differential geometry, the elements are united with all in their interrelations, stimulated by means of the historical past of the parallel postulate. starting with the traditional assets, the writer first explores man made tools in Euclidean and non-Euclidean geometry after which introduces differential geometry in its classical formula, resulting in the fashionable formula on manifolds comparable to space-time. The presentation is enlivened by way of historic diversions corresponding to Huygens's clock and the maths of cartography. The intertwined techniques may help undergraduates comprehend the function of trouble-free principles within the extra common, differential atmosphere. This completely revised moment version contains quite a few new routines and a brand new resolution key. New subject matters comprise Clairaut's relation for geodesics and using variations corresponding to the reflections of the Beltrami disk.

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