There are plenty of stained glass lamp shade pattern books and designs out there, and one could make the shade first and then find a base for it, or find a shade design pattern that comes closest to fitting the base that they already have.
But is there a formulaic approach to determining angles/sizing for a table lamp shade using 6 panels, 8 panels, or any number of panels where I know the top size of the cap that I want to use, I know the diameter that I want the bottom to be, and I know the height that the shade should be?
How do you figure out the sizes and angles in the each panel? Trial and error? Cut 6/8/whatever test panels out of paper and tape them together to see if they wrap around into the desired shape and dimensions? I suppose that the trigonometry that I learned in high school would have helped here perhaps, but is there an exact science to figuring this out?