These are double-pointed needles. They are size US 2-1/2 (3 mm).
They are pretty small, pretty sharp, and pretty slippery. I only have a couple of small sets of dpns, purchased a long time ago. Back in the day when I learned to make socks, I first learned from a book and that book said you had to use dpns, so I bought some and used them. I didn't like them very much.
Shortly thereafter I took a class on how to make socks with two circular needles and I liked that much better. The needles didn't poke me, they didn't fall out, they weren't as awkward to hold, and I didn't get the little ladders between the needles. Once I started with the circulars, I didn't look back and learned to easily convert any pattern written for dpns to circulars. This included finishing hats and doing mittens. I may have even said on occasion that I didn't use dpns and didn't know why anyone else would. That's me; never judgmental or anything!
However, when I was finishing my Geodesic cardigan and doing the sleeves in the round, I didn't like how the two circulars I was using were pulling the laceweight yarn and I had some issues with the "seam" area between the needles. So when I went to finish the child's pullover sweater that I recently made, I decided to try dpns for the sleeves. It was pretty easy because the needles were size 8 (5 mm) and were made from wood. Short, not too slippery, and quite substantial. It worked well.
I needed to make a quick baby hat to match the booties I made recently as a gift. I was using a cotton/acrylic blend yarn because the baby will live in the desert, so the yarn is pretty smooth. I had attempted a couple of hat patterns but wasn't getting the result I wanted, so I found another pattern and decided to use much smaller needles than I had been trying. I also decided (gasp!) to try it with dpns, since I thought this yarn would pull too much if I tried to use my usual technique. I looked in my needle boxes and came up with the aforementioned needles. I cast on and made my way up the hat with good success. The gauge was close and the size looked good.
The hat came out pretty cute.
So now what? Do I add dpns in every size to my collection? They were quite handy for this project, but it was small and quick. I don't think I'll ever go back to them for socks, since I had a few issues with pulling them out of the stitches, dropping the loose needle onto the floor, and having a needle just fall out on its own once the decreases were close to being finished. When you use two circulars, you pull the needle through on the long cable and let go after you finish each section. When you do that with the dpns, the needle comes out of the stitches and goes flying. Definitely not good for airplane knitting for me.
So, what did I learn? I can use dpns if I have to. They are useful in some instances. I need to practice in order to keep them in my hand and off the floor. Slippery needles and slippery yarns aren't a good match.
It's always good to learn something new.