ABSTRACT
Look at your feet. Are you wearing socks? Even if
you’re not, I’m willing to bet that at some time in your
life, you’ve worn socks. Most socks are knitted in the
round, which means that they are knitted in circular
rows. The mathematical implication for analyzing this
knitting is that if the rows have length 60, say, then
as soon as the knitter gets to 60, the next stitch is the
first stitch on the next row, or stitch number 1. That’s
like a clock. After 12 o’clock, we don’t just keep go-
ing on to 13 o’clock (unless we’re on military time), we
start over at 1 o’clock. Because of this special rule,
clock arithmetic works a little differently than regular
arithmetic. Similarly, the arithmetic for knitting in the
round works like clock arithmetic, rather than like reg-
ular arithmetic. Mathematicians call clock arithmetic
modular arithmetic.
