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- TL;DR Summary
- There is a simple geometric derivation of the area element in polar coordinates. Is there an algebraic derivation as well?

There is a simple geometric derivation of the area element ## r dr d\theta## in polar coordinates such as in the following link: http://citadel.sjfc.edu/faculty/kgreen/vector/Block3/jacob/node4.html

Is there an algebraic derivation as well beginning with Cartesian coordinates and using ## x=rcos\theta## and ## y=rsin\theta ## to transform the Cartesian area element ##dx dy##?

Is there an algebraic derivation as well beginning with Cartesian coordinates and using ## x=rcos\theta## and ## y=rsin\theta ## to transform the Cartesian area element ##dx dy##?