If you need a project for World Wide Knit In Public Day here’s a tiny baby hat:

It’s a traditional Scandinavian ‘Djævlehue’ in garter stitch with increases/decreases.

No seaming, a bit of grafting/Kitchener stitch, only two ends to weave in.

Traditionally this hat is knit flat and then seamed. After seaming the cast on and cast off edges together, the bottom zig-zag edges on the picture above are seamed together to form the hat.
I suggest suggest you join the seams together as you knit – a bit like doing short rows.

The beanie is knit sideways, from the middle of the back with little flaps for the ears and a super fit for the baby’s head.

When knitting you count only the purl rows on one side. It’s even easier if you place a marker in the rows between each increase/decrease section.

To make a preemie beanie you will need:

1 ball of very soft cotton (or superwash baby wool)
Knitting needles of a size that makes your knitting soft and loose
A spare length of yarn and a crochet hook

Start by crocheting 26 stitches with the spare yarn
Pick up 24 stitches with the beanie yarn and work 2 rows in garter stitch

1st section (right slanting):
Row 1: K1, M1, K20, K2t, K1
Row 2: K24
Repeat these two rows until you have 14 purl rows

2nd section (left slanting):
Row 1: K1, K2t, K20, M1. Then you knit the last stitch together with a picked up stitch from the side of the decrease a few rows below.
Row 2: Turn and K24
Repeat these two rows until you have 14 more purl rows and the two decrease sides are joined together

3rd section (right slanting):
Row 1: K1, M1 K20, K2t, K1
Row 2: K24
Repeat these two rows until you have 7 purl rows

4th section (left slanting):
Row 1: K1, K2t, K20, M1. Then you knit the last stitch together with a picked up stitch from the side of the decrease a few rows below.
Row 2: Turn and K24
Repeat these two rows until you have 7 more purl rows and the two decrease sides are joined together

5th section (right slanting):
Row 1: K1, M1, K20, K2t, K1
Row 2: K24
Repeat these two rows until you have 14 purl rows

6th section (left slanting):
Row 1: K1, K2t, K20, M1. Then you knit the last stitch together with a picked up stitch from the side of the decrease a few rows below.
Row 2: Turn and K24
Repeat these two rows until you have 14 more purl rows and the two decrease sides are joined together

Do not cast off.
Move the cast on-stitches from the crocheted yarn onto a knitting needle.

Using this excellent method of grafting with knitting needles join the seam at the back of the hat together. (Here’s another description of how to knit-graft)

Turn the knitting so each needle shows a purl row (and the knit rows are on the inside) before starting to graft.

Start the grafting from the rim of the hat so you can use the end of the yarn to fasten the tiny hole in the middle of the hat.

If you don’t know any preemies, give the hat to a charity!