For no good reason I decided to work out what shape minimized the tension at the attachment points of a draped cable. It turns out to be a lot droopier than one might expect. All of the details of the calculation using sympy can be found here.
I recently had the pleasure of finding a copy of the manual for my favorite calculator. I know it is incredibly nerdy to have a favorite calculator (and even more nerdy to read the manual), but it really got me thinking.