In many knitted hat patterns, the ribbing of the hat band is a decorative variation on ribbing. However, if the hat is long enough, that ribbing will be folded up when the hat is worn, hiding the pattern stitch. Here's an adjustment that can be made to most hat patterns to ensure the decorative side of a fancy ribbing is on the outside when folded up.
Work the ribbing as instructed (or planned, if you don't have a formal pattern). In the final round of ribbing, work to the last stitch of the round and wrap and turn. Then, working in the opposite direction, knit one round. When you reach the wrapped stitch, knit it together with the wrapped yarn. Proceed with the body of the hat as instructed in your pattern.
I've written before about making a scalloped hem in knitting by using yarn overs to create a natural fold-point, almost like a perforated line. The round of plan knitting does something similar and create a small, decorative ridge on the purl-side of the fabric when the ribbing is folded up.
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