This quick sweater was whipped up in a weekend, by first constructing a long oblong scarf, picking up stitches for a back in the center, and seaming the sides. Finally, I picked up stitches at the armholes and double-crocheted in the round. Because of the style of construction, it was easy to try on at each stage.
I couldn't find a tutorial online for a rounded edge, so I experimented a little. The neck and front piece was started with a long chain, then I double-crocheted around in a standard rectangle, like a traditional scarf started from the inside out. When I reached 8" width, I switched to a treble crochet. I achieved the round shape by increasing in the stitch just before and the stitch just after a corner. I did ch1 between increases, but I don't think that's really necessary. In any case, the bulky yarn I used (Lion Brand Scarfie in blue/black) was very forgiving and stretchable. This yarn is also one of the softest I've ever used and feels nice against my skin.
The back is very open, being completed in a treble crochet. The sleeves are double-crocheted, with 6 rows of alternating fpdc and bpdc at the wrists to form a ribbed border. I did attempt to matche the color gradation on the sleeves, though not very strictly. The fiinal result is a little shorter than I had planned, but still has a nice shape and a little looseness to allow the wearer to layer clothes underneath. I sent it back to Georgia as a gift for my godmother, who prefers to dress in black and blue. She had not been expecting it, but as you can see below it matches her outfit anyway.
For more cardigans, see this cocoon cardigan and this great starter pattern by Sewrella.