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Unformatted text preview: 2005 Dong Qian All Rights Reserved 1 MECH 321 Notes: Radius of curvaturehow it is derived In the class, I have intentionally skipped (or will, depending on when you downloaded this notes) the derivation of the relation between the radius of curvature and the first and second derivatives of a curve. This subject belongs to the topics covered in differential geometry, which was primary developed by Riemann (Yes there are two ns in it). Differential geometry is a great topic. Einstein used it as a tool to derive his famous theory of relativity (I heard that some of the work was partially done by his wife at the time, who is a mathematician). The basic idea in the differential geometry, if you want me to put it in the simple way, is to realize that the world (or the space) is not simply flat or straight, and study the properties with this new philosophy. There are a lot of books on it in the Math library, but I wont recommend you to start on it since it needs some preliminary, such as tensor notation, which will take some time....
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This note was uploaded on 10/13/2010 for the course MECH 321 taught by Professor Qian during the Winter '05 term at University of Cincinnati.
 Winter '05
 Qian

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