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In the previous article the author examined curves and surfaces. One might hope to continue by analogy in many dimensions. The concept of working in many dimensions is so bewildering (yet today so matter-of-course) that it needed the genius of Bernhard Riemann to show us exactly how it can be done. In just one lecture on the foundations of geometry he completely changed our way of thinking. Later geometers were to spend entire lifetimes trying to finish what Riemann had begun. Some even see the genesis of General Relativity in his lecture.
KeywordsManifold Quadratic Form Euclidean Space Principal Curvature Previous Article
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- J W Milnor. Lectures on Morse Theory, Annals of Math. Studies. No. 55, Princeton University Press, New Jersey, 1963. Book which deals with many topics covered here rather nicely.Google Scholar
- M Spivak. Comprehensive Intoduction to Differential Geometry. vol. II, Publish or Perish, Berkeley, 1970.Google Scholar