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A hat designed to protect you from the elements, for example, but made of mesh with a non-existent brim wouldn't quite hit its mark.
In a previous blog, "Picking the Right Cowboy Hat for You," we used the shape of the the wearer's face as a jumping off point to finding that perfect hat. That rule of thumb is especially good for cowboy hats.
But what about more casual hat-wear, like the fedora?
Take a look at the fedora and its cousin, the trilby (sometimes referred to as the "shirt-brim fedora" or "trilby fedora").
Like the fedora before it, the trilby was named after a fictional heroine in a late-19th century narrative — Trilby O'Ferral. It started off, like the fedora, as primarily a hat for the ladies, but quickly because appropriated by the men of that time. Both the trilby and the fedora enjoy cyclical resurgences in popularity.
Frank Sinatra, in his younger years, often wore a trilby, and a trilby was perfectly suited for his narrow, vertical-line frame. And this brings us our very simple recommendation for choosing a formal hat:
Cowboy hats notwithstanding, the brim of one's hat should be in proportion to his shoulders.
Men with broader shoulders would do best accentuating their frame with a fedora rather than a trilby. A trilby on gentleman with bigger shoulders could easily become too comical. (Sinatra had a narrow vertical-line aesthetic in his youth and could pull off a trilby.)