A magic formula for evenly distributing shaping
It's not really magic. It's algebra but maths is rather magical, especially when designing (or even altering) patterns means it's way more useful than you ever believed in high school.
Sometimes the number of decreases (or increases) you want to do divides neatly into the number of rows you have available. And sometimes it doesn't. In that case you have to do the decreases at two different rates (one higher and one lower than the average) or end up with a long straight section instead of a smooth diagonal.
Of course you can figure out how to distribute your shaping via trial and error or by plotting things out on graph paper. The problem with both of those methods is that they're time consuming, especially when you're grading a pattern for several sizes.
I've seen a simpler version of this formula in a few places. I think I first came across it in Maggie Righetti's Sweater Design in Plain English (an excellent resource if you have any interest in designing).
The problem was that it only worked if the difference between your two rates was 2. That will often be the case, but I found myself trying to something closer to a curve and for some sizes the optimum shaping was achieved by decreasing every row and every 4th row. I wanted a formula that would work whatever the difference between the rates was.
There was also a niggling line in Righetti's book:
"I'm not enough of a mathematician to know why you divide by 2. Just take my word for it that you do!" (p.179)
Oh I took her word for it, but I wanted to know why. And I figured that if I knew why maybe I could work out whether you could change the formula to work with different rates.
It turns out that you can alter the formula to work in all cases and in case you also want to know why it works I made a video:
Don't care about the why? Just plug your numbers into this formula. It will work as long as your lower rate of shaping is lower than the average rate and the higher rate is higher (within reason!).
And just the version with words rather than references.
I use this all the time when calculating patterns in a spreadsheet. It's fairly simple to write a formula that will take your available rows and required shaping and work out what the rates of shaping should be and how many times each should be worked. No more trial and error!