What Is Pi?

What is pi? If you’re so inspired, feel free to insert your own favorite punchline about delicious baked goods here. Although I’ll spare you the humor since we are, of course, not talking about that kind of pi (as in p-i-e). Instead, we’re talking about π (as in the sixteenth letter of the Greek alphabet). And our timing couldn’t be better since we’re fast approaching a pretty big holiday in the hearts of true math fans—pi day on March 14. Why all the fuss over a number? And why March 14? Stay tuned for the answers.

What Is the Meaning of Pi?

As you may have learned in school (but perhaps never fully appreciated), the origin of the number that we call “pi” for short (and usually write with the Greek letter π) that’s equal to approximately 3.14 has a very easy-to-understand meaning. To see what this meaning is, we’re going to do a little arts-and-crafts project that you can complete using nothing more than a piece of paper, a pencil, some string, and a pair of scissors. Or, if you prefer, you can actually do the whole thing in your head.

How to Draw a Perfect Circle

The first thing you need to do is use some string to help you draw a perfect circle on your piece of paper. Of course, no matter how hard you try your circle won’t be “perfect,” but if you’re careful you can do a pretty good job. To draw your circle, start by cutting about a 3-inch piece of string (or bigger if you’re working with a piece of paper that’s larger than a normal sheet of binder paper). As you’ll see, this string is going to represent the diameter of your circle. Now, draw a dot near the center of your paper and pin the middle of the string down right on top of this dot with your finger (you can find the middle of the string by folding it in half). Then hold the loose end of the string up against the lead of your pencil, pull it away from your pinned down finger so that the string is taut, and trace out a circle by moving the pencil around in a…well…circle.

How to Use Your Circle to Find Pi

Now that you’ve drawn that, take a long piece of string and use it to measure the circumference of the circle. In other words, lay the string out along a curved path on top of the circle and measure how long it needs to be to make it all the way around the circle one time. Once you’ve done that, carefully cut the string where it overlaps with the end of the string laying on the circle. The length of this piece of string you’ve just measured and cut is the circumference of the circle.

But what does this all have to do with pi? To see, start by laying that long piece of string representing the circumference of the circle out in a straight line. Then take the shorter piece of string representing the diameter of the circle (the one you used to help you draw the circle) and cut two additional pieces of string that are exactly the same length. Now line up these three diameter strings end-to-end along the circumference string and think carefully about what you see.

What Is Pi?

So, what do you notice? Well, first of all, the three diameters aren’t quite as long as the circumference. But we can also see that the circumference of the circle is quite a bit less than four diameters. Which means that we’ve discovered that the circumference of a circle is between three and four (but closer to three) of its diameters in length. If you use a ruler and measure things more precisely, you’ll find that the circumference is actually a little longer than 3.1 diameters. If you measure even a little more precisely, you’ll find that the circumference is actually a little longer than 3.14 diameters. And, as we’ll talk about in the future, you could keep going on and on making ever more refined measurements of this ratio.

Does the number 3.14 look kind of familiar to you? As you might have already guessed, that number is our dear pal pi. Which explains exactly why you memorized that formula in school saying that the circumference of a circle is equal to pi times the circle’s diameter (C = π x D)—because that’s exactly the formula we just discovered by looking at the lengths of our strings. And just in case you’re wondering if all of this depends in any way on the particular circle you draw, the answer is no. The ratio of the circumference of a circle to its diameter is always pi…no matter what circle you draw!

What Is Pi Day?

Believe it or not, that’s pretty much all there is to pi. You might even say that understanding the origin of the number pi is as easy as—wait for it—pie (sorry, I couldn’t resist at least one bad pun). But in truth that’s not really all there is to pi. In fact, there are other ways to think about the definition of pi, and there are a ton of other places where pi sometimes rather mysteriously shows up in the world of math. Which means there’s plenty of additional pi for us to look forward to enjoying in the future.

Finally, in case you haven’t heard, there’s a big holiday for math enthusiasts coming up. As we’ve literally seen in our arts-and-crafts project today, the value of pi is approximately equal to 3.14. If you get a bit creative and turn this number into a date, you get March 14. Which is why every March 14 math enthusiasts around the world gather together across the interwebs to celebrate and enjoy some pi. And the good news is that everybody is invited to celebrate in whatever way moves them. You can find out more at the official pi day home at piday org.

Wrap Up

Okay, that’s all the math we have time for today. Remember to become a fan of the Math Dude on Facebook where you’ll find a new featured number or math puzzle posted every weekday. And if you’re on Twitter, please follow me there too. Finally, if you have math questions, feel free to send them my way via Facebook, Twitter, or by email at mathdude@quickanddirtytips.com.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!