The first project for many knitters is a scarf, a long, rectangular scarf. Then they advance to shaped pieces that start as rectangles, but become sweater pieces. With circular knitting needles, they knit tubes, like socks or hats. Flat circles may be elusive to knitters, until they discover that knitting icon Elizabeth Zimmerman applied the geometry of Pi to make a flat, circular shape.
Cast on nine stitches onto one double-pointed needle. Distribute the stitches on three DPNs, three stitches on each needle. Join the stitches into a round, making sure not to twist them.
Knit one round. Go slowly, as this can be a little difficult with all the needles. It helps to lay the needles down on a flat surface.
Start the next round with a yarn over. Knit the next stitch. Repeat this for the rest of the round. This is an increase round. You now have 18 stitches, six stitches on each needle.
Knit three rounds with no increases. Repeat the increase round. You now have 36 stitches, 12 on each needle.
Knit six rounds with no increases. Repeat the increase round. You now have 72 stitches.
Knit 12 rounds with no increases. You can also start knitting with the 16-inch circular needle. Repeat the increase round. You now have 144 stitches.
Knit 24 rounds with no increases, then an increase round. Your total number of stitches is 288. When your stitches get too crowded on the circular needle, start with the 24-inch circular needle.
Knit 48 rounds, then an increase round. There will be 576 stitches. The circle will be about 72 inches across, depending on the yarn and gauge.
Knit one or two more rounds, and bind off loosely.
Put a ring marker on the DPN with the first stitches. When you switch to the circular needle, move the marker between the first and last stitch to mark the beginning of the round. You can, of course, stop at any point for a smaller circle. To make a large circle, just double the number of rows between each increase round. The cast on leaves a small hole in the centre. You can use the tail of the yarn to sew the hole closed if it bothers you.