Yes, I’m late, but I’d be remiss in my nerdly duties if I ignored Pi Day (also Einstein’s birthday!) completely.
I was introduced to the concept of pi when I was just a wee little geeklet, and I remember thinking that the joke “pie are not round, pi r squared!” was absolutely the funniest thing ever. My sense of humor hasn’t changed all that much; now my favorite joke is the one about two cats of the same mass and which one will be the first to slide off of a slanted tin roof.
But in a belated celebration of pi day, I should talk about something circular now.
What distance does a wheel travel when it makes one full rotation? This is something that I have talked about both in my former job as a physics teacher and in my current job as a math tutor. Many students will correctly intuit that the distance traveled is equal to the circumference of the wheel. But how can we make the idea concrete?
With toilet paper, of course. If you want to see the distance that a wheel covers as it rolls, you need something that leaves a trail. I would take a roll of toilet paper, point the tube toward me, and draw a line down the side of the roll. Then I’d put the roll on the table with the tube pointing toward the class and the ink mark pointing straight down to the table. I’d unroll the roll until the mark was pointing straight down to the table again, showing that the roll had completed one full rotation. How far did it go? The length of the toilet paper that was unrolled = the distance between the ink marks = the amount of paper needed to wrap around the roll once = the circumference. This solidified the idea for students, plus the toilet paper gave them enough tissue to blow their noses on for weeks.
So next time you see your cat unrolling your toilet paper, don’t chastise him. He’s just exploring rotational motion.