Just learned about this: Traditional hatters used a pair of tools called a conformer and a formillion to ensure hats perfectly fit their clients.
The conformer captures the client's head measurements in a math-free way, marking a paper template. That template is then used to position a series of dies in the formillion. The hat is then placed over the formillion and steamed into shape:
Here's the longer version, with narration:
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Paul's Hat Works in San Francisco used this on me to make my cool bowler hat. They're not cheap, but my confomer profile is stored with them, so if I ever get an urge to get another bowler, or perhaps a top hat, I don't even have to be there to get a a hat that fits perfectly.