Integral is a worsted-weight, snug-fitting beanie worked from the bottom up. Using only about 130 yards of the main color and less than 30 yards of the contrast color for even the largest size, it is a great way to use up some leftover yarn and make a quick gift to keep somebody warm. A pattern of both colorwork and texture adds intrigue without being too difficult and a decorative Latvian braid separates the brim from the main hat for an elegant touch.

The design was inspired by the integral, a basic component of calculus in which you find the area between the curve of a graph and the axis on which it is plotted. The basic idea behind the integral was developed independently around the world, stretching as far back as 370 BC Greece and 250 AD China but wasn’t formalized into its modern form until the 1800s. Today the integral is indispensable and one of the first tools physicists learn in order to understand the world.

Difficulty: Beginner to Intermediate

Required Skills: Knit stitch, Purl stitch, Stranded colorwork, Decreases, Working in the round, Latvian braid (instructions in pattern)

Sizes

1 2, 3 {4, 5, 6}

To fit heads of circumference 16 17.5, 19 {20.5, 22, 23} inches

The hat is stretchy, so size down if you are between sizes.

Materials

Yarn: 50 60, 80 {90, 115, 130} yards worsted weight yarn in Main Color (shown here in Knit Picks Brava Tweed in Stratus)

10 12, 15 {18, 22, 26} yards worsted weight yarn in Contrast Color (shown here in Knit Picks Brava Tweed in Goldenrod)

Needles: US size 8 12” circular needle, or size needed to obtain gauge for main body of hat 30” circular needle (for magic loop) or double pointed needles the same size as your gauge needles, for shaping the crown

Notions: Yarn needle

Optional, but recommended: six stitch markers, one of which is distinct for the beginning of the round

Gauge: 18 stitches and 22 rounds = 4” in stockinette stitch after blocking

Finished Measurements

Circumference: 14.75 16, 17.25 {18.75, 20, 21.25} inches

Height: 6 6.5, 7.5 {8, 9.5, 10.5} inches