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history-page28 - Differential Geometry • What is it ◦...

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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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