A practical application of the principle can be found here.

The round ripple (RR) crocheted afghan is a thing of beauty and math! Being curious, I decided to find a simple method of determining the rate of increases to make a RR with different number of points and stay flat without curling into a tube or waving. The rule of thumb has long been established that you increase 12 stitches per round when using worsted weight yarn and double crochet and this will create a flat circle.

As a refresher, a round ripple afghan has peaks that are created by increasing 2 sts at the points and the valleys are formed by decreasing 2 sts.

To make an increase row, 2 additional increase sts are needed per peak; therefore, a 12 point RR requires that the increase round increases the stitch count by 24.

So 12/24 = a ratio of 1:2 or increase 1 of every 2 rounds. (12 is the number of necessary incs per rnd and the 24 is the actual number of incs per round on a 12 point RR)

One inc round incs 24 sts then one round has no increases so this averages out to 12 increases per round. Perfect….but what if you want a different number of points?

Let’s carry this further:
pls note the abbreviations below: + is inc rnd, - is a rnd w/o incs

24 points = 12/48 = 1:4 = inc 1 of every 4 rnds
(+---) repeat these 4 rounds

20 points = 12/40 = 3:10 = inc 3 of every 10 rnds
(+--+--+---) repeat these 10 rnds

18 points = 12/36 = 1:3 = inc 1 of every 3 rnds
(+--) repeat these 3 rnds

16 points = 12/32 = 3:8 = inc 3 rnds of every 8 rnds
(+-+--+--) repeat these 8 rnds

14 points = 12/28 = 3:7 = inc 3 rnds of every 7 rnds
(+--+--+) repeat these 7 rnds

12 points = 12/24 = 1:2 = inc 1 rnd of every 2 rnds
(+-) repeat these 2 rnds

10 points = 12/20 = 3:5 = inc 3 rnds of 5 rnds
(+-+-+) repeat these 5 rnds

9 points = 12/18 = 2:3 = inc 2 rnds of 3 rnds
(++-) repeat these 3 rnds

8 points = 12/16 = 3:4 = inc 3 rnds of 4 rnds
(+++-) repeat these 4 rnds

7 points = 12/14 = 6:7 = inc 6 rnds of 7 rnds
(++++++-) repeat these 7 rounds

6 points = 12/12 = 1:1 = inc every round
(+) increase every round

Isn’t this a simple method of making your own RR patterns? Now you can make a 6 to 12 to 24 point RR without the edges making large waves! With 6 points, inc every round, after you add 6 more points to make 12 points, inc every other rnd, add 12 more points to total 24 points, then inc once every 4 rnds. How about a 5 to 10 to 20 point RR? Even when using someones written pattern, this formula will help you see if there is potential for problems long before you put your RR in the frog pile.

Reminder--this is an approximation only. Your needle size, yarn weight, and tension may affect this “rule of thumb”. Omit or add increase rows as it becomes evident they are needed. For those of you who excel in math, there is a calculus formula that is more exacting.

OK, so you ask, what about a 5 point RR?

(notice: have not tried this with 5 points as it is theory only and maybe this is where the rule begins to degenerate and besides there are 5 point rr patterns available, but here it is anyway)

5 points = 12/10 = 6:5 notice this ratio is lopsided? you would need to have 6 inc rnds for every 5 rnds--not possible; but, it is possible to make double the number of increases for 1 round of the 5 rnds:
(++)++++) or inc 20 sts on one round and then 10 sts on the next 4 rnds. (60 sts inc’d for 5 rnds or 12 sts per round which meets the general rule of thumb!)

As your circumference gets quite large, you will need to increase more often.

Try this and if you have comments/suggestions, let me know!

Here is another great tip: To check to be sure your RR afghan will be flat, as work progresses, periodically fold your work in half and if it doesn’t form a crescent shape, it should lay flat. Don’t hesitate to add or decrease the number of inc rows as necessary!

Don’t want holes? Instead of using a V stitch and Double V stitch for the points, use a small shell (3dc) and a large shell (5dc) for the non inc and inc rnds.

For no holes in the valleys, use dec sts such as dec dc making 1dc out of 2dc twice.

Would this formula work on shapes such as a pentagon, hexagon, heptagon, octagon, etc? Don’t see why not….

NB:
avg for worsted weight yarn in dc is inc 12,
hdc is 8 and sc is 6 for each round.

The algebraic formula can be found here