The top of the hat features tapering triangles. This hat is a ladies small size (it fits my head). You can change the size of your hat by casting on more or less stitches in multiples of 12. I made my hat on the short side with 1” ribbing (5 rounds for me). You can make yours a little longer by making the ribbing section longer, up to ~3” if you want it to be a fold-up brim.

Hat matches the Pythagorean Reversible Scarf
http://www.ravelry.com/patterns/library/pythagorean-reversible-scarf

Stitch patterns used in this pattern are mentioned in the Pattern Post here:
http://smariek.blogspot.com/2007/10/pythagorean-hat-scarf.html
and also in the Pattern Bibliography post here:
http://smariek.blogspot.com/2007/11/pattern-bibliography.html
.