Essential sewing tool: physicist

I was trying to think how, when making a hat, you’d shape the crown piece when it has to fit the smaller circumfrence of the crown at the top, and the larger circumfrence of the brim at the bottom. So I asked my tame and friendly physicist, who produced the explanation above. Since so much about patternmaking is about mathematical modelling (3D forms into 2D versions) I highly recommend y’all get yerselves a physicist.