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How to Celebrate Pi Day!

Hello everybody! Before I start, let me just say that I apologize for my two-week break. I've had some really cool math experiences in the last two weeks that I'd love to write about in future articles (I have some great stories to tell!), but they've also kept me from writing a GLeaM article lately. I'm back now, and I won't be going anywhere anytime in the foreseeable future. In fact, given everything that's happening with school closures, I may be posting even more than once a week now, so you may just see even more content moving forward!

Today, I'm writing on a Saturday instead of a Sunday for one reason. It's Pi Day! I'm going to give you all of my ideas of what you should do to celebrate Pi Day and lots of resources so you can explore all that you want to know about pi today. This will be a bit of a random collection, but I hope it's enjoyable for you on this mathematical day.

Calculating Pi

What better way to celebrate Pi Day but to calculate pi? There are so many fun ways to go about arriving at 3.1415926535... so here are a few for you!

1. Try the traditional way. Take any circle in your house, and measure across the diameter. Then, take a string, wrap it around the circle and measure the distance around the circle (the circumference). All you need to do now is divide the circumference by the diameter, and you'll get pi. In fact, the more precise you make your measurements, the closer to pi you'll get. You can even make it a competition to see who can get pi to the most digits.

2. Measure pi with pies! Hopefully, you bought an apple or peach pie for this special occasion, so measure its circumference and diameter. Or better yet, get a ton of pies and make a giant circle with them:

3. Use an infinite series of numbers. It turns out that the infinite series

1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 equals π/4, so feel free to add together a bunch of odd fractions if you have nothing else to do today. All you got to do is multiply by four when you finish!

You can even use this famous series (aka the Basel Problem) to calculate pi:

1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + ... = π^2/6

Isn't it super crazy that adding a bunch of fractions (aka rational numbers) together gives us not only an irrational number but the circle constant itself! Both of these equations blow my mind a little bit when I see them. I'd love to prove them for you but for the most part, they both require calculus. I can give you a brilliant non-calculus proof of the second one with this video though:

(Yes, if you've been paying attention, this is one of my favorite math videos from my other article!)

4. Try Buffon's Needle Problem. Find a needle, measure its length and draw horizontal lines on the floor so they're two needle lengths apart. It turns out the probability of a needle falling on a line is 1/π, so test it out! Do a bunch of trials, divide the total number of trails by the successes and then take 1 over your answer! If everything works out, you'll get π!

The setup looks like this:

Screenshot courtesy of MindYourDecisions

Here's two videos on this problem. (Yes, there's some calculus, but you don't need any of it to try the problem!)

5. Discover your own way! There are so many ways to calculate pi. Here are a few more of my favorites:

Use a pendulum:

Use completely random numbers:

Use a dartboard:

Do it the Archimedean Way! Essentially, build polygons with an increasing number of sides both inside and outside of a circle and use the perimeters as under- and overestimates:

There's a lot of creativity when it comes to calculating pi, so all of you are perfectly capable of inventing your own ways. Think critically, and tell me what you come up with in the comments.

Learn About the History of Pi

You can't have Pi Day without learning a bit about pi. From the ancient Babylonians to Archimedes to modern math, there are tons of related stories and facts, so take a moment to learn about pi today.

Here's some of my favorite articles:

Go to! Yep, there is such a thing., and here's a great article:

And here's a great video:

If you want even more to read, I recommend Why Pi? by Johnny Ball for younger grades and A History of Pi by Petr Beckman for older grades.

I won't leave you hanging here without telling you at least one story!

My favorite absurd pi story comes from the state of Indiana where the state government in 1897 tried to legally set the value of pi to 3.2! An amateur mathematician named Edwin Goodwin in Indiana thought he solved an ancient problem called Squaring the Circle, a proof he was so proud of he tried to copyright, but implicitly in his proof, he assumed the value of pi was 3.2. The bill went super far in the legislative system there, and it was even passed unanimously in the Indiana House of Representatives. Completely by chance, a mathematician happened to be at the room at the time, so he was able to convince the Indiana Senate to throw it, and the bill failed, but yet, pi was almost changed to 3.2! It turns out that society blunders a lot too, and when it comes to pi, there are no exceptions:

I'll also mention that today is Albert Einstein's Birthday as well, so read a little about him too:

Watch Some Videos about Pi

I've given you plenty of videos already, but I thought it would be fitting to add this section again. So many math channels release amazing pi videos yearly, and there is so much great content out there, so go exploring! If you've heard of tau, there are also plenty of debates between if we should use pi or tau (=2π), and those are always fun to watch as well.

I'll give you three to check out here, but look for more!

Eat Some Pie!

This one goes without saying. Apple, pumpkin, peach, key lime, whatever makes you happy! Today's a day to splurge. Eat as much pie as you can, but don't forget the mathematical origins of this day!

That's it! Have a very happy Pi Day everybody, and feel free to suggest more ideas to celebrate today in the comments!

Cover Image courtesy of Nerdist and all videos courtesy of their creators



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