A common construction method in crochet is to begin at the center of a shape and work in the round (either a coil or in rounds, it doesn't matter), increasing outward. The number of stitches on average that you increase in each round determines whether the piece will lie flat. And what that magic number of increases is depends on what stitch you are using or is predominantly used in each round. Your gauge also matters, since working with a loose gauge means your work will stretch, and that creates wiggle room when it comes to your numbers.
In single crochet, you need an average of six increases per round to lie flat. I've demonstrated what that looks like with the green swatch in the image below. Note that it is a hexagon, since I made my six increases equidistant and had them in every row. I could have achieved the same thing by having three double increases around to create a triangle, or I could have done a triple increase four times around, every other round, to make a square or rectangle. You can also increase a lot in one round and then work without increasing until everything evens out again. That's one way of making something circular, like the first dishcloth pattern in this post.
The number of stitches I started with is not important. In fact, crocheted, top-down garments are generally worked this way, just with more stitches at the beginning to create the neck hole.
If you have too many increases per round, your work will eventually start to ruffle, and any points or corners will get pointier than they are supposed to be. You can see that in the red swatch on the right in the image above. In that swatch, I increased eight around in single crochet, instead of six. You can see, especially at the top, due to the lighting in the photograph, that the swatch is a little ruffled. If you look closely, you can also see that the corners of the octagon are more pronounced than they should be. I made this swatch bigger than the green one, because I wanted to emphasize that feature.
The next two swatches were made in half double crochet. The lower one had eight increases per round, and you can see that it started to cup pretty quickly. The upper swatch had ten increases per round, and it lies flat. These two swatches are the same number of rounds across. If you don't have enough increases per round, your work will eventually cup. It might not happen as obviously or quickly as it did with the lower swatch, but it will happen.
Sometimes you might want something to cup a little bit. Practical Crocheter's Basic Top Down Hat uses seven increases per round in half double crochet, and her Heavy Single Crochet Watch Cap increases five per round in a variation on single crochet. In both cases, having the crown of the hat being somewhat rounded makes the hat more "hat shaped" and less basket shaped, like it would be if the crown were flat.
Double crochet lies flat with twelve increases per round, as you can see in the image below, on the left. However, once you get to double crochet and other tall stitches, you have enough stitches per round that it takes longer for cupping or ruffling to show up. In a classic granny square, for instance, there are usually 16 increases per round, but you have to make a fairly big granny square or work in a pretty tight gauge before the extra increases become apparent. Usually, the extra stitches in a granny square make themselves known by the corners torquing (being too pointy) and the square not being strictly rectangular when you fold it in half. If you keep making your granny square bigger beyond that point, it eventually starts to ruffle.
The last swatch (above, right) was done in treble crochet. It has 18 increases per round, and it lies flat, but I could tell that it would eventually start to cup. Treble crochet actually works best with 20 increases per round, but the stitch is tall enough that you have significant wiggle room with it, and you have enough stitches that the presence or absence of those extra two stitches per round takes a while to accumulate to something visible.
If you are working in the round in a pattern stitch, the number of increases you need are dependent mostly on the average height of the pattern stitch. In the Round Waffle Stitch Baby Blanket, the frequent use of front and back post stitches make the rounds a little shorter than straight double crochet. Since I wanted something approximately round, and the increase technique I used adds three stitches per increase point, I increased 24 every other round, which averages out to increasing 12 every round, just like I would for double crochet. However, the shorter pattern stitch meant that increasing 24 every other round was a little too much, and I had to add a few extra non-increase rounds throughout the piece.
This post has been linked to Your Moment, Busy Monday, Senior Salon Pit Stop, The Stitchin' Mommy, and Thursday Favorite Things.
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