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008			220909b |||||||| |||| 00| 0 eng d
020			_a9780521133111
037			_cTextbook
040			_aCSL _beng _cCSL
041			_aeng
084			_aB6 Q3 TB _qCSL
100			_aMcCleary, John _9863108
245		0	_aGeometry: From a differentiable view point
250			_a2nd
260			_aCambridge, _bCambridge University: _c2013.
300			_axvi, 357p.
500			_aBibliography 341-350p.; Symbol & Name index 351-353p.; Subject index 354-357p.
520			_aThe development of geometry from Euclid to Euler to Lobachevsky, Bolyai, Gauss, and Riemann is a story that is often broken into parts – axiomatic geometry, non-Euclidean geometry, and differential geometry. This poses a problem for undergraduates: Which part is geometry? What is the big picture to which these parts belong? In this introduction to differential geometry, the parts are united with all of their interrelations, motivated by the history of the parallel postulate. Beginning with the ancient sources, the author first explores synthetic methods in Euclidean and non-Euclidean geometry and then introduces differential geometry in its classical formulation, leading to the modern formulation on manifolds such as space-time. The presentation is enlivened by historical diversions such as Hugyens's clock and the mathematics of cartography. The intertwined approaches will help undergraduates understand the role of elementary ideas in the more general, differential setting. This thoroughly revised second edition includes numerous new exercises and a new solution key. New topics include Clairaut's relation for geodesics, Euclid's geometry of space, further properties of cycloids and map projections, and the use of transformations such as the reflections of the Beltrami disk.
650			_aDifferential geometry _9863109
650			_aGeometry _9863110
650			_aMathematics _9863111
700			_aMcCleary, John _9863108
942			_hB6 Q3 TB _cTB _2CC _n0
999			_c7354 _d7354