i am ridiculously mediocre at crochet, and this is the first pattern i've ever attempted to put into a format where others might be able to use it. it might be terribly confusing and/or stupid, and i would urge you to contact me or write something in the guestbook with questions or clarifications.
ch 1 (does not count as 1 sc), work 6 sc into ring. (6 st)
sl into first sc of last round, ch 2, 1 dc in same sc, 1 dc in next sc, 2 dc in following sc. * 2 dc into next two sc, 2 dc in next one sc. repeat from * until the end of the round. (note: you will not make it to the end of the round perfectly) (8 st)
sl into first dc of last round, ch 2, 1 dc in same dc, 1 dc in next two dc, 2 dc in following dc. * 3 dc into next three dc, 2 dc in following one dc. repeat from * until the end of the round. (10 st)
sl into first dc of last round, ch 2, 1 dc in same dc, 1 dc in next [round number - 1] dc, 2 dc in following dc. * [round number] dc in next [round number] dc, 2 dc in following one dc. repeat from * until the end of the round. (note: i went until 25 because that is when my hat fit onto my head pretty tightly, but do more or less for however large your head is)
sl into first dc of last round, ch 2, 1 dc in same dc, 1 dc in next [(# of dc in last round) / 2]. 1 hdc in remaining dc.
sl into first dc of last round, ch 2, 1 dc in same dc, 1 dc in next [same number that was inserted last time]. 1 hdc in remaining dc.
sl into first dc of last round, ch 1, 1 sc in second st from hook, sc in next two st. * ch 1, sc in second st from hook, sc in next two st. repeat from * until the end of the round.
the same exact thing you did in round 2.
the same exact thing you did in round 37 or whichever row in your hat that corresponds to 37.