One of my day jobs, at least. I put this together for a thematically appropriate Pi Day quiz for the site that I work for. If you haven’t played a Word Ladder quiz before, the concept is that each correct answer changes exactly one letter from the previous answer.
…and, thanks to the magic of post scheduling, this post is going up at exactly 9:26AM on 3/14/15.
To be honest, I initially wasn’t sure what my Pi Day post should be about. I’ve already written about pie and circumference; what aspect should I cover now? The answer struck me as I recalled a question on a job application I filled out recently. I was asked what my educational philosophy was and how I had demonstrated this in previous positions. After years of studying and working in education, my response felt hackneyed, but it really is my philosophy: people learn better when they see and experience concepts rather than just memorizing facts and formulas. This requires hands-on activities and real world demonstrations. So how can we apply this to pi?
The essence of pi is that it’s the ratio between the circumference of a circle and its diameter. We don’t have to put blind faith in this formula, because we can test it for ourselves.
You will need:
- a variety of round objects
- a flexible tape measure (think sewing box, not tool box) OR ribbon, a marker, and a ruler
1. Take a round object. Use the tape measure or ribbon to measure across the diameter of the object; if using the ribbon, mark the length of the diameter with a marker and use the ruler to measure this length.
Emerald City Comic Con (ECCC) is this weekend, and, while I can’t attend myself (I work weekends and I always wait till GeekGirlCon to request time off), I’ve been helping a friend with her Lady Sif costume. With no pattern to work from, our primary job was to look at photos and make posterboard templates of Lady Sif’s armor, which were then traced onto thin foam, cut out, and covered in metallic fabric.
She’s an artist and I’m definitely not. But my experience as a math tutor means I can draw polygons decently, so I started with the six quadrilateral abdominal plates. When we laid the first few templates that I made against the base of the costume, we found that I had the shape right. However, the size was definitely off. I needed to make the templates smaller, but I didn’t want to change the overall shape- I wanted my new shape to be similar to my old one. When two polygons are similar, all of the angles in one shape are the same as the angles in the other shape, and the length of each side has been multiplied (or divided) by the same factor.
I trimmed the appropriate amount off of each side. While the result looked good against the base of the costume, my friend noted that the new template was a lot smaller than the old one. Intuitively, we think that whatever happens to the side lengths of a polygon should be the same thing that happens to the area of the polygon- if each side length is cut in half, the area should be cut in half, right?
One of the most difficult things about teaching math and science is figuring out interesting and accurate ways to make concepts concrete.
Solutions frequently involve pie. I have used pie to explain everything from the extremely straightforward (how to calculate the area of a sector of a circle) to the less tangible (the amount of thermal energy in an object depends on both its temperature and its mass). Bill Nye has used pie to demonstrate the transfer of momentum. Mixed-variety pies can show how ratios work; while my examples generally include more mundane flavors such as apple, banana, and cherry, the ratio of “crack” slices to candy bar slices to cinnamon bun slices in Momofuku’s “frankenpie” is 2:1:1. This ratio doesn’t definitively tell you how many slices there are, but it does tell you that the total number must be a multiple of 4. (I’ve never had this pie and it looks delicious, but the price is awfully steep. Maybe I could use it in a tutoring session and write it off as a business expense?)
I’d write more- the pies-as-science possibilities are endless- but for some reason I’m suddenly ravenous. Pardon me for a moment.
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.