Pi Is for Circles

This post is for crocheters.

How to crochet circles

Here is how to crochet something round:

Chain three stitches.

  1. With a single crochet stitch, connect the last stitch to the first.
  2. Single crochet in each of the two remaining chain stitches. You should now have three single crochet stitches at the edge of a tiny circle.
  3. To start the next row, keep going in the same direction: Single crochet two stitches in each of the single crochet stitches from the last row. When you finish this row, there should be six stitches on it.
  4. For the next row, crochet two single crochet stitches in each of the six single crochet stitches from the last row. Now you should have 12 stitches in the row you just finished.
  5. Keep going until your circle is the size you want, increasing 6 stitches with each row, spreading the increases out evenly over the row, placing the increases away from the earlier increases. (If you just keep increasing at the same point on every row, you will get a hexagon. )
  6. When you have the size you want, slip stitch the last row. This row has no increases.

There is your circle. A coaster, maybe.

Why this works

A circle’s circumference, the distance around the circle, equals \pi times the circle’s diameter. “\pi” (a Greek letter, pronounced “pi”) is a number that is equal to about 3.14.

A stitch in single crochet is just about “square,” meaning it’s as high as it is wide. (This is approximate.)

Each stitch increases the circle’s diameter by an amount equal to the distance that the stitch covers in that row of the circle. Let’s call that distance “s.”

Each time you complete a row you increase the circle’s diameter by a length of 2\times s.

Since circumference equals \pi times diameter, when you increase diameter by 2\times s, you also increase circumference by 2\times \pi \times s. Each stitch increases the circle’s circumference by a length of s, so you need to make each round 2\times \pi \times s longer than the one before.

That means you need each row to have 2 \pi more stitches than the row before it has. That’s 6.28 more stitches.

How can you make 0.28 stitches? This is crochet; relax and ignore the 0.28. Then each row needs to have six more stitches than the row before it has.

Note that no matter how big your circle gets, the number of stitches you add to each row does not change. To keep adding rows to the circle just keep adding six stitches per row.

Interesting aside

Imagine that the Earth is a perfect sphere and you run a thread all the way around it at the equator. Then you lift the thread one inch everywhere. How much additional three do you need to make the end meet the beginning?

This is just the crocheted circle extended to the scale of the Earth. To lift the thread all around the planet you need 2\times \pi more inches of thread. That’s 6.28 inches of extra thread to lift the rope 1 inch all the way around the Earth.

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