Archimedes by Matt Babcock
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Archimedes

Knitting
Works with any yarn provided minimum gauge can be met
see notes below
200 - 350 yards (183 - 320 m)
Variable; minimum head circumference 17 inches
This pattern is available as a free Ravelry download

This hat is knit as a long skinny strip that is distinctly non-hatlike. Short rows give the strip curvature so it can be coiled into a three-dimensional spiral without wrinkles or tucks. When you join the selvages together with a single spiraled seam -- eureka! You end up with a marvelous beret, to the delight of your admirers and the chagrin of everyone who refused to believe that you were making a hat.

The design of the hat is based on a geometrical figure called an Archimedean spherical spiral. The hat and the spiral are named for the Greek scientist/mathematician/inventor Archimedes, who described this type of spiral in the third century BCE. Scholars have reached no definite conclusions as to whether Archimedes was a knitter and what kinds of hats he preferred.

The pattern gives instructions for two sizes. The difference between the large and small sizes is in the overall diameter. Either size hat can be made to fit almost any head. The large hat is floppy and dramatic. The small hat is somewhat more demure.

Have fun with your choice of yarn! The pattern is based entirely on the dimensions of the knitted fabric rather than on counting stitches or rows. Provided you meet these minimum requirements for gauge you can use anything you like:

large hat: at least 18 stitches per 4” in stockinette
small hat: at least 20.5 stitches per 4” in stockinette

Row gauge for either hat should be in the range of 1.2 to 1.6 times your stitch gauge. Most knitters’ row gauges fall into this range more or less automatically.

The pattern includes a chart of approximate yardage required based on gauge and yarn weight.

Let me know how it goes -- I’d love to see pictures!