In which I prove my mastery of junior high geometry

I was contemplating the Elizabeth Zimmerman Pi Shawl, of which I've knit about a million, and I always forget the basic formula. So the thing I do know thanks to six years of university-level math is the formula for the circumference of a circle, which is:

C = Π2r

Where r = the radius, which is the distance from the center to the edge of a circle.

Now, when knitting a circular bit of knitting, each row increases the area of the circle in all directions, threfore, the radius isn't as applicable as the diameter, which is the distance from one edge of of the circle to the edge directly on its opposite.

The diameter of a circle is:

d=2r

So the circumference of a circle can be expressed as:

C=Πd

Thanks to the beautiful mathematical mystery that is the Algebraic Distributive Property, the every time the diameter of a circle doubles, so does the circumference! Check it out:

2(C) = 2(Π) x 2(d)

So what does this mean for my knitting? It means that to knit a perfect circle, you need to increase to twice the number of stitches every time you double the number of rows since your last increase round. For example:

Cast on 8 stitches in the round.
Knit three rounds.
K1, yo to end of round, 16 stitches.
Knit six rounds.
K1, yo to end of round, 32 stitches.
Knit twelve rounds.
K1, yo to end of round, 64 stitches.

...and so on, and so on, until you run out of yarn or your hands fall off, whichever comes first.