The Mathematics of a Granny Circle (inc pattern)

I had made a few demo granny squares to work out the best way to do them and the best size hook. Now I decided I wanted to see how to do a granny circle.

But the big questions were: how to start? and how to work the increases?

I knew that the centres of a granny square and the centre of one of the hexagons for the hexagon blanket had involved twelve trebles, so that seemed a good place to start.

I decided that doing four standard grannies (= 3 trebles [US dc]  followed by a chain) might make the circle too square so I thought six double trebles with chains between might be better.

Now for the maths.

I decided that the circumference of each of my granny circles should be measured in chains as that was what the circumference would effectively consist of.

Well the circumference of a circle is 2πr (π = 3.1416… but since you can’t have fractions of a chain I decided to call it 3).

So circumference would equal 6 x radius.

Three chains are what normally substitute for a treble [US dc] so calling a chain ‘c’ and a treble ‘t’ we get 3c = t

So measuring the radius of the first row we get  6 x t = 18c. This accorded very well with my idea of six double trebles with chains since that would give exactly that number.

Now the second row.

When doing granny squares (or stripes, or circles) the trebles overlap so effectively each row only adds about two chain to the radius. So calling this distance t’,  t’ = 2c.

This would be 6 x (2t’) = 6 x (4c) = 24c.

Now lets start thinking of grannies (= 3 trebles [US dc)] followed by a chain) and lets call a granny ‘g’ so g = 4c.

So circumference of second row circle should be 24c = 6g.

That’s good as it would mean working one granny between each of the treble pairs.

Third row

Would work out as 6 x (3t’) = 6 x (6c) = 36c = 9g

Fourth row

Would work out as 6 x (4t’) = 6 x (8c) = 48c = 12g

Fifth row

Would work out as 6 x (5t’) = 6 x (10c) = 60c = 15g

So are we seeing a pattern here?

From row three the numbers must go –

9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60………………

I did try working exactly that number of grannies in each row for a few rows but it gave a rather distorted circle so I thought again.

*     *     *     *     *     *     *     *     *     *     *     *

We started with the idea that six is more circular that four, but twelve is even more circular. (Think of clocks and decorating cakes).

So – noting the rows that divide by twelve (bold) and those that only divide by 6 but not twelve (italic) we get:-

Rows 3 4 5 6 7 8 9 10
Grannies 9 12 15 18 21 24 27 30
Rows 11 12 13 14 15 16 17 18
Grannies 33 36 39 42 45 48 51 54
Rows 19 20 …………
Grannies 57 60 …………

Deciding it was easier to scrunch grannies up than stretch them out, I therefore decide to work twelve grannies for rows three and four.

Working rows three and four

So I worked two grannies into each of the gaps on row two and then one granny into each of the gaps on row three.

Rows five onwards

Well I could have tried working eighteen grannies into row five but remembering that when I worked Lucy’s pattern for a flat circle made of trebles, increasing every 11th treble worked so you hardly noticed it wasn’t a perfect circle.

I decide to try just increasing (by working two grannies into a space) so the rows were multiple of twelve, and as it worked well on rows three and four, to anticipate the increases.So this is what I did and as it worked well, that is what I settled for.


So row five increased the number of grannies to 24 (see above).

And this number was kept till row eight (see above).

On row nine to increase the number of grannies to 36, I could no longer increase equally into each space but had to increase every other space (see above).

But the circle was so big now it seemed to work.

As you can see from our pattern above, I now increased every fourth row, working twelve increases evenly into the row.

When working a granny square I like to work the three chain (treble equivalent) into the middle of an increase as it is less obvious that way. But in this case I was working the increases into the first gap on the relevant rows because it made it easier to do the count. However if I did it again, I think I would try to go back to starting in the middle of an increase.

My granny circle had really started out as just a sampler but I liked it so much that I made it into a table centre.

Finishing off with a nice symmetrical scallop edging.

So my pattern is:-

[I am using UK terms.]

  • Start: Ch 4 and join with a sl st into the first ch or you could use the Magic Loop method.
  • Row1: Working into ring: 3ch {=1st tr}, 1tr, 1ch, then repeat (2tr, 1ch) 5 times and join to third chain of start of row with a sl st.
  • Row 2: Working into the gaps between treble groups: 3ch {=1st tr}, 2tr, 1ch, then repeat (3tr, 1ch) 5 times and join to third chain of start of row with a sl st.
  • Row 3: [This is an increase row]. Into first gap 3ch {=1st tr}, 2tr, 1ch, then (3tr, 1ch, 3tr 1ch) into each of next 5 gaps then 3tr, 1ch into first gap and join to third chain of start of row with a sl st.
  • Row 4: Work as Row 2 but there will be 12 gaps in total instead of 6.
  • Row 5:  Work increases as Row 3 but there will be 12 gaps in total this time.
  • Rows 6&7: Work as Row 2 but there will be 24 gaps in total this time. From now on the increases = (3tr, 1ch, 3tr 1ch) are spaced out with single groups of (3tr, 1ch) in between.
  • Row 8: Work a half increase = (3ch {=1st tr}, 2tr, 1ch) into the first gap then a single group = (3tr, 1ch) into the next gap and an increase = (3tr, 1ch, 3tr 1ch) in the following one. Continue, alternating single groups and increases till you get back to the first gap and work 3tr 1ch into this and join to third chain of start of row with a sl st.
  • Rows 9-11: Work as Row 2. There will be 36 gaps in total.
  • Row 12: Similar to Row 8 but with two single groups between each increase.

Continue, making 12 increases in every 4th row until the desired size is reached.

Edging

  • Row 1: Work 2ch {=1 dc} into first st then 1dc into each following stitch (not spaces). Join with sl st into second chain at start.
  • Row 2: On this row sl sts are worked over the gaps and shells over the 3tr groups. I used a smaller hook because of only missing one stitch rather than two between middle of shell and sl sts. Repeat (sl st, miss a st, 4tr into next st (a shell) , miss a st). Join to first sl st at end and break off yarn.

I like to use a 5mm hook for granny squares for a blanket as that makes them softer but for the granny circle I used a 4.5mm hook and a 3.5mm hook for the second row of the edging.

This was with DK acrylic yarn.

For those who find such things useful here is a chart I made for myself:-

This has been tough to proof read so if anyone notices a mistake, please let me know.

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Published by

Rainbow Junkie

I am a retired mother of three and grandmother of five. I mostly knit and crochet while I watch television. I also love cooking and have dabbled in various other crafty things. I am crazy about: Rainbows, Butterflies, Flowers, Bees, Honey, Hexagons, Snowflakes, Symmetry, Mathematics and Dragons

25 thoughts on “The Mathematics of a Granny Circle (inc pattern)”

  1. Hello,
    This is a beautiful pattern. I love the color changes, very cheery and bright. Just what I need in gray old January 2014.
    I would like to let you know that in the US sc=single crochet, dc=double crochet which is what you have done here. Tr or Treble Crochet is triple crochet. So if you say 5t or 5tr it means 5 triple crochets. Its not a big deal, triple crochet will just give a lighter lacier look. Either way it is beautiful. I have been looking for ideas on using up my yarn and this is definitely on the list. Thank you also for the diagram. I have found that these diagrams are easier than written instructions in some cases. It is hard to find patterns written like this though.

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    1. Thanks for the info re US is triple not treble. The pattern I have written is in UK terms but I am sure you can translate. I do tend to do my more recent patterns in UK and US terms. But I must check if I get the triple crochet / UK double treble wrong.

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  2. Fantastic pattern! I found some beautiful yarns on sale today and want to do up a throw for my loveseat. This is the perfect pattern for this! Going to use a deep violet bulky yarn! Thank you for taking the time to post such fantastic instructions!

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  3. Thanks for the pattern. It is excellent. I like math and how much I use it in crochet, so I really enjoyed that part, too. Fantastic job! Thanks again, Sandy

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  4. Thank you so much for this … I will persevere with it .. although I am 61 and have dyscalculia ie .. maths and arithmetic are just a nightmare for me. Of course, having a maths besom, I mean teacher, in high school who would show us something new, ask ‘Any questions ?’ and when I put my hand up she would simply yell at me to sit down and tell me I hadn’t been listening ! (Needless to say, I shocked her rigid along with the class and myself when I found I understood how to work algebra !! lol ! Weird but true! I have to say I haven’t had a lot of chances to use it so it’s lost now in the mists of time !!)

    Your designs and explanations are very clear. THANK YOU !

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    1. Well I use maths all the time when I am crafting. But this post was partly for fun in showing how you can use maths to help with designing crochet items since I know lots of people are bemused by mathematics. Glad you mastered algebra and surprised your teacher! Algebra is much more mathematics than arithmetic. When I went to university to study mathematics, I did a course where we were told we would not need to be able to count beyond 11!

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  5. To the dearest one…my name is Ann and I m writing to u as I was fed up…I repeat totally fed up looking for perfect granny circle on the net…I was searching since past 40-45 days but cudnt find a satisfying one…some circles were great at d start but later it used to give me some different hexagon shape…I really thank god bcoz I came across ur pattern on Pinterest and reached ur blog and started n within 3 days I completed one circle. I m really thankful n grateful for ur help…thank you sooooooooo… much… I wish i cud send u d pix of my first granny circle…i m very happy as i have got the perfect round 😀 love ❤ ann

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    1. Hi…I wud need your help for half granny circle with the same pattern…I don’t get along with maths above 😦 Pls suggest something.
      As far as full circle is concerned I have gone up to round 20 and it’s jus perfectly going great with being flat..no errors …jus as u mentioned above about the increases…I m following the same n believe me it’s great. But I wanted to try a half circle with same pattern pls help 🙂

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      1. The pattern was never designed to be able to be turned into a half circle. However the thoughts that come to me are that you would obviously have to reverse direction every row and that you would need to work half as many stitches in each row as a full circle. Exactly how you would start and end each row is another matter. Maybe you should experiment. I am not feeling great at present as I have a bad cold but I hope this points the way.

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  6. I, too, searched a long time for the perfect granny circle, and I love this pattern. I’m having a bit of trouble with the edges curling up and in. Am I doing something wrong or will that resolve itself when the border goes on? I am making a rather large circle to be used as a blanket. Thank you!

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    1. I have only made a granny circle the size shown and I don’t remember having any problems. It is possible that if you make the circle really big the fact that I was approximating with my maths will mean the formula doesn’t work anymore.
      But I am thinking you mean that the outer edge doesn’t lay flat because it is not long enough. This could be because your chains in between the three treble groups are too small. They need to be as big as the top of a treble.
      If you spread your circle out on a flat surface (such as the floor) you should be able to see if it will lay flat naturally. If not you will need to adjust.
      The solution could be to increase on the third row, at least when necessary to keep it flat.

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