In yesterday's post, I wrote about how to create a gradient with evenly-spaced rings. Today's post is related. It still involves center-out circles and geometry.
Let's say you want to make a center-out circle. You have a pile of yarn that is all the same color, so you aren't concerned with rings or gradients or color effects. You just want to know how big a circle you can make with that pile of yarn. Is there a quick way to find out without playing yarn chicken?
The area of a circle = π r2
If we draw concentric rings, we can think about how much yarn is in each ring as compared to the whole project.
Recall our math:
π 12 = 1π
π 22 = 4π
π 32 = 9π
π 42 = 16π
π 52 = 25π
π 62 = 36π
π 72 = 49π
π 82 = 64π
π 92 = 81π
π 102 = 100π
Another way of thinking about this is a circle that is twice the diameter of another will have four times the area. A circle that is three times the diameter of another will have nine times the area.
What does this mean for yarn usage and project planning?
Start by weighing the yarn. Then begin knitting (or crocheting) the center-out circle.
When you have used 1/100th of the yarn, stop and measure the circle. If continued, you should be able to knit (or crochet) a circle 10 times larger than the current one. You should be able to work 10 times the number of rounds. As with gauge swatches, making measurements over small areas can introduce larger errors. But, you can keep checking your work.
At 1/100th multiply diameter by 10.
At 1/81st multiply diameter by 9.
At 1/64th multiply diameter by 8.
At 1/49th multiply diameter by 7.
At 1/36th multiply diameter by 6.
At 1/25th multiple diameter by 5.
At 1/16th multiply diameter by 4.
At 1/9th multiply diameter by 3.
At 1/4th multiply diameter by 2.
(For those of you who want decimals, the progression for multiplying yarn weight on your calculator 1/100th = 0.01, 1/81st = 0.012345679, 1/64th = 0.015625, 1/49th = 0.020408, 1/36th = 0.02777778, 1/25th = 0.04, 1/16th = 0.0625, 1/9th = 0.11111111, 1/4th = 0.25.)
In the diagram above, the pink circle is one unit across, the blue circle is two units, and the green circle is three units. That means if you were knitting those circles and it took 1 skein to make the pink circle, it would take 4 skeins to knit a whole circle the size of the blue one or 9 skeins to make a whole circle the size of the green one.
The reality is that unless I were working with a very large quantity of yarn, I wouldn't trust my reading at the 1/100th mark. But I might trust my reading at the 1/9th mark. And I'd certainly trust the 1/4th mark. So you should be able to get an idea whether or not that shawl will really be the size you want — or whether you have enough yarn to knit all 300 rounds in the shawl pattern — without having to do a lot of knitting and then face the heartache of losing at yarn chicken.
And as with the concentric circles I discussed yesterday, this method also works with center-out squares, neck-down triangles, and half-circles.
Let's say you want to make a center-out circle. You have a pile of yarn that is all the same color, so you aren't concerned with rings or gradients or color effects. You just want to know how big a circle you can make with that pile of yarn. Is there a quick way to find out without playing yarn chicken?
The area of a circle = π r2
If we draw concentric rings, we can think about how much yarn is in each ring as compared to the whole project.
Recall our math:
π 12 = 1π
π 22 = 4π
π 32 = 9π
π 42 = 16π
π 52 = 25π
π 62 = 36π
π 72 = 49π
π 82 = 64π
π 92 = 81π
π 102 = 100π
Another way of thinking about this is a circle that is twice the diameter of another will have four times the area. A circle that is three times the diameter of another will have nine times the area.
What does this mean for yarn usage and project planning?
Start by weighing the yarn. Then begin knitting (or crocheting) the center-out circle.
When you have used 1/100th of the yarn, stop and measure the circle. If continued, you should be able to knit (or crochet) a circle 10 times larger than the current one. You should be able to work 10 times the number of rounds. As with gauge swatches, making measurements over small areas can introduce larger errors. But, you can keep checking your work.
At 1/100th multiply diameter by 10.
At 1/81st multiply diameter by 9.
At 1/64th multiply diameter by 8.
At 1/49th multiply diameter by 7.
At 1/36th multiply diameter by 6.
At 1/25th multiple diameter by 5.
At 1/16th multiply diameter by 4.
At 1/9th multiply diameter by 3.
At 1/4th multiply diameter by 2.
(For those of you who want decimals, the progression for multiplying yarn weight on your calculator 1/100th = 0.01, 1/81st = 0.012345679, 1/64th = 0.015625, 1/49th = 0.020408, 1/36th = 0.02777778, 1/25th = 0.04, 1/16th = 0.0625, 1/9th = 0.11111111, 1/4th = 0.25.)
In the diagram above, the pink circle is one unit across, the blue circle is two units, and the green circle is three units. That means if you were knitting those circles and it took 1 skein to make the pink circle, it would take 4 skeins to knit a whole circle the size of the blue one or 9 skeins to make a whole circle the size of the green one.
The reality is that unless I were working with a very large quantity of yarn, I wouldn't trust my reading at the 1/100th mark. But I might trust my reading at the 1/9th mark. And I'd certainly trust the 1/4th mark. So you should be able to get an idea whether or not that shawl will really be the size you want — or whether you have enough yarn to knit all 300 rounds in the shawl pattern — without having to do a lot of knitting and then face the heartache of losing at yarn chicken.
And as with the concentric circles I discussed yesterday, this method also works with center-out squares, neck-down triangles, and half-circles.
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