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What Is Pi?

Learn what the number pi means using a simple arts-and-crafts project. Then find out why you’ll want to celebrate this newfound knowledge on March 14.

By
Jason Marshall, PhD,
Episode #097

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!

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