How to Find the Center of a Circle (and Save Christmas)
Ever needed to find the center of a circle? It’s one of those things that seems easy – until you have to do it. But rest assured there is a trick to figuiring it out, and it’s indeed fairly simple. Keep on reading for Math Dude’s quick and easy method!
Jason Marshall, PhD
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How to Find the Center of a Circle (and Save Christmas)
Have you ever noticed that cutting pie, cake, pizza, or anything else that’s round is hard work? Unless you’re really careful, that all-important first cut tends to miss the center of the circle. And that can be a serious slip-up, because it throws everything from that point forward totally out of whack.
Case in point: The Math Dude Thanksgiving gathering of 2014.
The perpetrator? Let’s call him “Bob,” to protect his identity. The weapon? An ordinary kitchen knife. The accused crime? Butchering the all-important first cut of the achingly beautiful, feast-topping pumpkin pie. The verdict? Guilty of doling out huge wedges of delicious pie to approximately half the gathering, and sadly-small slivers to the rest—including one “Math Dude.”
Today, we’re going to talk about how you can avoid this mishap and save yourself from future holiday misfortunes. What’s the secret? It all comes down to finding the exact center of a circle. And that, math fans, is precisely what we’re going to learn how to do today..
How to Find the Center of a Circle
Finding the center of a circle is one of those things that seems like it should be really easy to do – until you’re faced with the problem of doing it. Sure, you could just stab out a guess at where the center is, but that’s how “Bob” got in trouble cutting the pie in the first place, remember? Which means there must be a better way to do it.
Actually, there are a number of relatively simple ways to find the center of a circle. Before we get to pies, let’s think about finding the center of a circle you’ve drawn on a sheet of paper. Of course, if you were to draw a circle on a sheet of paper, you’d probably use a compass—which means you’d already know the location of the circle’s center. But let’s pretend you don’t already know it, and let’s think about what you could do to find it.
Method #1: Circumscribe a Square
Our first method begins by drawing a square around the circle. Technically, this is called circumscribing the circle with a square—which is just a fancy way of saying that we draw a square so that each of its four sides just touches the circle.
Of course, the tricky part of doing this is making sure that the square is actually a square – in other words, making sure that each of its four angles are right angles. One way to do this is to use the 3-4-5 triangle method that Knot Dude used when helping his ancient Egyptian father, Papa Knot, build the foundation for the Great Pyramid. What, you’ve never heard that story? Then you need to check out the Math Dude episode called Why Is Algebra Useful?
Once you’ve used Knot Dude’s method and have a ship-shape square circumscribed around your circle, all you have to do is draw a straight line from the top-left corner of the square to the bottom-right corner, and from the top-right corner to the bottom-left. The point at which these two diagonal lines intersect is the center of the square. And it’s also the center of the circle.
Method #2: Inscribe a Rectangle
But that’s not the only way to do it. Instead of circumscribing a square around the circle, you can instead start by inscribing any rectangle of your choosing within the circle. As you can probably guess, the term “inscribe” is another one of those fancy math words that simply means you draw the rectangle inside of the circle in such a way that each of its four corners (or vertices) just barely intersects the circle.
Again, the trick here is to draw an actual rectangle with proper right angled corners. But as before, once you’ve accomplished that, all you need to do is connect the corners of your rectangle with straight diagonal lines. The point where these two lines cross is the center of the circle.
Notice that this method works no matter what the rectangle you inscribe within the circle looks like. It can be tall and skinny, short and wide, or even a perfect square—so long as it’s an actual rectangle, it’ll work.
How to Find the Center of a Pie
While either of these methods work great for circles drawn on paper, neither seems well-suited for cutting pies. In truth, my Thanksgiving guest “Bob” really shouldn’t have needed to call upon either of these methods to slice the pie evenly. A bit of care, caution, and attention to detail usually does the trick.
But just in case you really want to be super-precise about things, here’s how you could use the math we’ve uncovered to locate the center of your next holiday pie. First, you need a round pie pan and a square baking dish to neslte the pie pan into. Then, when you’re ready to cut the pie, just put the round pan inside the square dish and use our first method to locate the center of the pie with as much precision as you’d like.
The end result should be a beautiful, evenly, and deliciously sliced pie that everybody will enjoy. But even if you, me, “Bob,” or anybody else happens to have another pie-cutting mishap in the future (because it can and will happen to all of us!), it’s good to remember that we can always go back for a second sliver. So, no hard feelings, “Bob.”
Wrap Up
OK, that’s all the math we have time for today.
For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.
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!
Pumpkin pie image courtesy of Shutterstock.
About the Author
Jason Marshall is the author of The Math Dude’s Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.