Pattern Writing and Applied Maths: Some Words on Decreasing, Row Spacing, and Multipliers

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This post was inspired by the age-old chestnut of writing pattern instructions. It’s a humble reminder that there is no such thing as perfect communication; nor will your words be understood by everyone, no matter how much effort you apply. 

Today’s post is all about knitting patterns and applied maths. I’m sharing how I approach the maths behind shaping over a given number of rows to form neck edges, sleeve caps, and any curved edge that requires the knitter to decrease with several changes of pace or rhythm. I hope this is insightful and helpful, if not thought-provoking!

To begin, here’s a table to demonstrate the relationship between text you’re likely to see in an English language pattern and the mathematical processes used to calculate the instructions:

Pattern text	Row spacing	Stitches to decrease	Total rows to work	Cumulative total rows
Decrease 1 stitch at neck edge of every row 6 times	1	6	6	6
Decrease 1 st at neck edge of every alternate row 6 times (every RS row)	2	6	12	18
Decrease 1 st at neck edge of every 4th row 3 times (every other RS row	4	3	12	30
	MULTIPLIER	MULTIPLICAND	PRODUCT

To explain the mathematical terms:

First up: A text explanation

• The MULTIPLIER is the number with which we multiply – in this case, row spacing;
• The MULTIPLICAND is the number to be multiplied – here, stitches to be decreased;
• The PRODUCT is the result obtained when multiplier meets multiplicand – here, it is the total rows during each stage of decreasing, or when each multiplier is active.

The row spacing is important because it contains the most IMPORTANT information – your multiplier.  If you don’t know this, then you have no way of mathematically tracking your work. It is also important to see it in case you have any pattern queries.

It also means that you can be more confident about keeping track of your work. You now have maths to support your comprehension of the written instructions.  And as we all know, written instructions can take many forms, whereas numbers cannot.  Integers have a far less subjective interpretation. It’s a bit like writing a computer programme.

Four and five don’t jive. So if your row spacing is 4, i.e., something needs to be done on every 4^th row, you are safe in the knowledge that 5 will be nowhere near the interval between decreases.  5 is not in the 4 times table! Unless we’re talking about common multiples like 20 or 40, when they say “hi” as they pass in the street.

Second: A visual explanation

Here is a numerical diagram of what decreasing on every 4^th row looks like (image from SplashLearn https://www.splashlearn.com/math-vocabulary/multiplication/multiplier):

With neck shaping, the preparatory row – i.e., the row during which you divide the work and put the stitches on hold to work one side at a time – is generally on the RS of the knitting. If we relate this to the diagram above, we are on zero (0).

Subsequently, the numbering for neck shaping is that the WS row is always 1, or odd-numbered, and the RS row is always 2, or even-numbered. Here you have another emphasis on even numbers to back up the even multipliers you’ll deal with when working your shaping.

Why the multiplier is the key to knitting patterns and applied maths

Further, the multiplier also tells you the rows on which the decreases fall throughout any given area of row shaping.  That is – referring to the table above:

• We’ve begun with decreasing six times on every row, i.e., WS-RS-WS-RS-WS-RS. This is the first group of decreases.
• If WS/odd-numbered rows begin with 1, and the next part of the instruction is to decrease on every RS row (or every alternate row), then in all cases that is the second (2^nd) row following the final decrease.
• Since the final decrease of the first decrease group was on the RS, or even-numbered row of the knitting, i.e., row 6, it follows that any decrease with an even-numbered row spacing will also fall on the RS.
• Consequently, in this second 12-row group, which features decreasing on every alternate row, the decreases will fall on rows 2, 4, 6, 8, 10, and 12 – with the final decrease being worked on row 12, the product of the multiplier and multiplicand.
• For the next decrease stage, phase or rhythm – every 4^th row – we again determine the row position of the next decrease in relation to the last decrease worked, and also by the row multiplier.  If we know that we’re working with multiples of 4, the decreases can only fall on rows 4, 8 and 12 of the following section, i.e., 3 x 4.  We also know that we can only be working with even-numbered or RS rows, because WS rows have been designated as odd-numbered. Remember, we started our neck shaping on the WS of the knitting, so that was row 1.

The row spacing is the multiplier (and is typically an even number in knitting patterns)

Understanding that the row spacing is a multiplier helps to eliminate misunderstandings in pattern writing. These include hiccups such as working 4 rows between decreases, instead of decreasing on every 4^th row. Again, refer to the diagram above. 

Think of it as taking steps. Next time you get up and walk, notice (not for the first time, I hope!), that your legs and feet alternate as you put one foot in front of the other.  If you count your steps, you will notice that one foot always touches the ground on the odd-numbered steps, and the other foot always touches the ground on the even-numbered steps. 

The only way you can disrupt this is if you hop on one side – but that just reverses the position of the odds and evens.  They will still be in alternate harmony.

Multiplication => patterns => where knitting meets maths

Speaking of harmony, you may have noticed that the multiplier column follows a pattern of its own. This is one that pops up repeatedly in knitting patterns.  When shaping a curve, the row spacing or decrease rhythm always doubles.  Regardless of tension, this rhythm tends to produce a smooth curve – 1, 2, 4. 

If you’re musical, it’s not unlike the time value slowing down from quarter notes, to half notes, to whole notes. (Or crotchets, minims or quavers if you’re from the UK and/or over a certain age, or had a teacher who was over a certain age! 😉). 

I always follow this pattern when drafting neckbands, and 95% of the time when drafting sleeve caps.  Decreases that are frequent, rapid, or close together in row terms form a sharper angle or deeper curve than those spaced further apart.

So there we are!  I hope that this was helpful, if not interesting 😊.

And if you want to go one step further and take a deeper dive into knitting patterns and applied maths, I have a taster course for you!

And if you found this post helpful, please share it on social media or pin it to Pinterest so that other knitters can find it. Thank you 🙂

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