Simply beautiful: Finding the covariant basis from seemingly nothing

[latexpage] Seeing how I wrote a new post yesterday in the area of tensor analysis, I was reminded of the beautiful result below. It likely would have made it onto this blog at some point, so I thought I would quickly write it all out. Here we go. *** Imagine we are presented with some …

Understanding metric elements for cylindrical coordinates

[latexpage] The metric tensor is ubiquitous when arriving at a certain level in one's physics career. When it comes to cyndrilical coordinates, there is a useful way to remember its deeper meaning through a rather simple derivation - or at least through the use and construction of a series of definitions. (I say 'simple' in …