Did you happen to buy Joan Sallas' hat book Hut Auf!, e.g. during the Mennorode 2004 convention? Or you have the Spanish version Origami Papiroflexia: CORROS DE PAPEL. Have you also tried to figure out the correct size of the paper for a hat that fits?
OriCalculators
With this page you can calculate the size of the more awkward rectangles
from Tomoko Fuse's Origami Design, thanks to
Dennis
Walker.
On his own website, Dennis has an Excel file that does
these same calculations.
Sometimes you need a strange proportion, and you don't have the correct paper.
Thanks to
Dennis Walker you can now
calculate a more convenient proportion.
On his own website, Dennis has an Excel file that does these same calculations.
Thanks to Dennis
Walker you can now calculate a number of common paper sizes
very easily.
On his own website, Dennis has an Excel file that does
these same calculations.
Enter the size in the field below, the possible sizes will be calculated automatically. When you start entering the calculations will be displayed.

On pages 222 and 223 of his Origami Omnibus Kunihiko Kasahara explains the proportions of various polygons. These are used on the subsequent pages to create various polyhedra.