My Math Forum Connection between cesaro equation and polar coordinates

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 February 28th, 2014, 05:47 PM #1 Senior Member   Joined: Nov 2013 Posts: 137 Thanks: 1 Connection between cesaro equation and polar coordinates First, I'd like that you read this littler article (http://mathworld.wolfram.com/NaturalEquation.html). The solution given by Euler that coonects the system cartesian (x, y) with the curvature ? of the "cesaro system" (s, ?), is that the derivative of the cartesian tangential angle ?* wrt arc length s results the curvature ?. However, in the 2D plane is definied the polar tangential angle ?* too. Thus if I want express a curve given s and ? in terms of r and ? (or vice-versa) I need to establish a connection between the curvature ? and the polar system. So, would be correct to say that the derivative of ? wrt s is equal to ?? * https://en.wikipedia.org/wiki/Tangential_angle https://en.wikipedia.org/wiki/Subtangent https://en.wikipedia.org/wiki/List_o....A0ro_equation EDIT:

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