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Unformatted text preview: Differential Geometry What is it? The study of the properties of curves, surfaces, and their generalizations. The study of the geometry of spaces in which the distance function is prescribed in- finitesimally. The early forms of differential geometry stemmed directly from the invention of the Calculus (and were practically indistinguishable from it). Applications like cartography also played a large part in its development. The term differential geometry was apparently not coined until 1894. Newton Along with Huygens (but working independently and using different methods), he stud- ied involutes, evolutes, and curvature of plane curves. An involute of a curve is the curve traced by the end of the cord that is originally placed along the first curve and then unwound. An osculating circle for a curve at a point on the curve is the circle passing through that point that best fits the curve....
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.
- Fall '10