Pi Day Shenanigans #π   7 comments

Pi

It’s Pi Day, Pi Day, Gotta Get Round on Pi Day! Everybody’s looking forward to diameters! Diameters!

Alright, so this post isn’t so much about gaming. So sue me. However, it *IS* about Pi! And really, who doesn’t appreciate Pi? I’m a big fan of promoting the maths and sciences, and Pi Day is a great day to do so. So here are a few tricks, a few facts, a few nonsensicles, etc. all about our favorite irrational constant. (Sorry e, they haven’t made an e day yet)

A History of Pi

3.141592653589793238462643383279502884197169399375105820974944592307816406…

Pi (π) is, simply put, the ratio of a circle’s circumference to it’s diameter. Pi is considered an irrational and transcendental number that never ends and never repeats. The exact person or date the ratio was discovered is lost to the ages. There are those that suggest that since the Great Pyramid of Giza has a ratio of the perimeter of the base to the pyramid’s height that comes close to 2π, that the Egyptians have known of pi since the pyramid’s building between 2589 to 2566 B.C. However, this may also just be a coincidence of the efficient design the Egyptians used.

However, a Babylonian tablet from around 1900 to 1680 B.C. *does* calculate pi to 3.125. The Rhind Mathematical Papyrus of 1650 B.C. calculates pi to 3.1605. Pi is even roughly approximated in the King James Bible, in 1 Kings 7:23 in which is being described the construction of a temple by King Solomon:

And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.

30 cubits (an ancient unit of length, the distance from your elbow to the tip of your middle finger) circumference / 10 cubit diameter = 3. Not bad.

It wasn’t until Archimedes, around 250 B.C. started using multi-sided polygons that it changed from being an educated guess to what we know it as today. Using geometry it became more and more refined starting with Archimedes, then mathematicians Ptolemy, Hui, Chongzhi, Aryabhata, Fibonacci, al-Kashi, Viete, Roomen, Ceulen, and Snellius. Pi was refined more and more until Christoph Greinberger, using the same polygonal method, came to 38 digits of Pi in 1630 A.D., which remains the most accurate approximation manually achieved using polygonal algorithms.

Then came the era of infinite series, or using the sums of terms of an infinite sequence, and more refinement by mathematicians such as Somayaji, Madhava, Gregory, Leibniz, and Wallis. Isaac Newton and Leibniz’s discovery of calculus in the 1660′s led to even more refinement.  Abraham Sharp using infinite series calculated pi to 71 digits, finally surpassing Greinberger’s 38. Machin came around in 1708 with a new method that reached 100 digits, and his method culminated in Ferguson’s 1946 620 digits.

Then came the computer era. Around 1949, Wrench and Smith using a desk calculator, reached 1120 digits. Technology kept progressing and the number snowballed finally reaching 1 million digits in 1973. As of 2011, the number of found digits, as I’m sure has been beaten by now, is up to 10 trillion digits.

The funny thing is that as far as functional computations go, no more than 39 digits are necessary, as that is the amount needed to accurately calculate the volume of the known universe to a precision of one atom. We had that in the 1600′s.

So What Use Is Pi To Me?!!!!

That’s all well and good, sure, but what use does the average person need Pi for?!! Well, math is essential to all of our lives. Sure, you may not need it on a daily basis, but you know of it and so probably use it unknowingly. For example, here’s a favorite bar bet on mine:

A height of ~ 3.75 in.

Which is Taller, The Height of My Cup, or it’s Circumference?

Say you’re in a bar. Take your pint glass, or any cup, really, turn to the person next to you and say: “Hey, for the next drink, I bet you are terrible with distance.” If you don’t get punched, take your glass and ask which is longer, the circumference of the top of the cup, or the height. A person who isn’t fluent in math will generally say the height… and they are incorrect. A person who is fluent in math will say the circumference. And they’d be right. “Cool”, you say. And then start stacking. Put under the glass your cell phone, a pad of post-its, etc. and keep asking. Eventually, they’ll say “Okay. The height is bigger.”

The height of the stack finally matches the circumference of the mug, at ~10.5 in.

… and most likely, unless you really put a ton of stuff under it, they’d still be wrong. It’s funny like that, our brains tend to overestimate vertical height, and underestimate horizontal length. The circumference of my mug? ~10.5 in. (Forgive the inadvertent advertising, this is just some of the stuff I have around me… I like tea.)

Get More Pizza For Your Buck

So, pizza, right? Who doesn’t like pizza? Hot sauce and melted cheese over a thin, crispy crust is the thing of gods. So simple, and yet, so complex. But should you get a medium? Should you get a large? How much MORE pizza does an extra 4″ really giving you?

As it turns out, a lot.

I took the menu to a local pizza place and compared some prices, all inches listed are for the diameter of the pizza:

10″ Personal Cheese Pizza – $7.75

14″ Medium Cheese Pizza – $9.75

16″ Large Cheese Pizza – $10.99

Using the simple formula for the area of a circle:  Area = π * (radius)^2, we can calculate the total area of the pizzas. And really area is what we’re going for, as that is a true determination of the quantity of pizza you’re getting.

10″ Personal Cheese Pizza – $7.75 – A = 78.5 sq. in. = 10.13 sq. in. / $

14″ Medium Cheese Pizza – $9.75 – A = 153.86 sq. in. = 15.78 sq. in. / $

16″ Large Cheese Pizza – $10.99 – A = 200.96 sq. in. = 18.29 sq. in. / $

Well damn. Look at that. If we use the Personal Pizza as a baseline, we see that the Medium pizza is almost twice the size! The large is not as big of a difference, and is only 2.5 times the size of the personal and only ~30% larger than the medium. However, even if you get the large, you’re still getting the most pizza for your dollar.

Your results may vary, depending on what your local places charge, but most likely the results will end up about the same. Also it depends on how hungry you are. If you’re only hungry for 78 sq in of pizza, by all means don’t pay more for wasted food.

Speaking of Pizza…

I’ve definitely seen this make the rounds, but to figure out the Total Area of a Pizza, you use…. PIZZA! Crazy!

We aren’t talking about the area of a circle, though, but the area of a cylinder. Afterall, pizzas have height, too.

The formula for the area of a cylinder is thus:

Area = π * (radius)^2 * height

If the radius = z, and the height = (just roll with us here, these are totally legit substitutions) then:

The Area of a Pizza becomes: Pi * z * z * a

BOOM!

Test the Speed of Your Computer’s Processor

Occasionally I build computers. So far, I’ve built them for myself, for friends, and for family, but I definitely know my way around the interior of a PC box. Not too long ago, I upgraded my system to a nice, probably overkill, but wicked Core i7-3770 Quad Core processor. It is a thing of beauty. I had upgraded from a much older AMD Dual Core, and wanted to know exactly what kind of upgrade I had received. Sadly, the exact figures have been lost to time, but let’s just say it was a very healthy difference.

I found out, though, using a very simple benchmark program that involves, you probably have guessed it by now, calculating Pi! It’s called Super Pi, and it simply calculates how long it takes your processor to calculate to 1 million digits of Pi. In fact, you could even tell it to keep going, but most time 1 million is enough to get a decent benchmark, and with today’s computers it’ll be done in seconds. Go ahead and put your system through it’s paces, too. A medium-end system generally takes about 15 minutes to calculate 32 million digits.

Einstein

Other Fun Pi Facts

π – The Alt-Code for the greek symbol representing Pi is Alt-227. Just hold down Alt and type ’227′, and Pi will appear on your screen.

π – All in a bid to improve math and science in our country, in 2009 the United States House of Representatives designated March 14th as “Pi Day”. July 22nd is even designated as “Pi Approximation Day”, as sometimes 22/7 is used to approximate it, but we don’t really want to celebrate an approximation, right?! (Oh wait… since Pi can never be fully calculated, we use an approximate, huh? Ah well.)

π – Pi Day is also Albert Einstein’s Birthday! The man, the myth, the legend.

π – My wife and I celebrate the day we started dating on February 7th. If we were to give other transcendental irrational numbers days, then February 7th would be “e Day”! How awesome is that?! (e ≈ 2.71…)

π – Salvadore Dali was a big fan of the irrational Pi and used a lot of mathematical principals in his art. The Dali Museum in Flordia even celebrates Pi Day in his honor with all kinds of events!

Wow

Longest post ever? Yeah, but so it goes. If you made it here to the end, please have some pie! Compliments of CSTM.

So go out, my awesome readers, and see the wonder and the majesty that is Pi. Appreciate the history, the search for knowledge, get more pizza than you can eat, check out a Dali painting or two, build a computer, and win a bet.

Happy Pi Day all!

// Ocho

P.S. – Pi Day Shenanigans has also been brought to you by Math Happens. Follow it on Twitter at @YouGotMathed. Why? Because You Just Got Mathed!

Sources: 

Happy Pi Day: Fun Facts About Our Favorite Irrational Number

Bible Gateway: 1 Kings 7

Wikipedia: Pi

Wikipedia: e

Wikipedia: Cubit

The roles of altitude and fear in the perception of height

Today I Found Out: The Mathematical Volume of a Pizza is Pizza

www.SuperPi.net 

The Dali Museum, Calendar

www.Alt-Codes.net 

CNET: National Pi Day? Congress Makes it Official

Wikipedia: Pi Day

7 responses to “Pi Day Shenanigans #π

Subscribe to comments with RSS.

  1. So if Pi is the ratio of the diameter to the circumference of any given circle, and ratios in math are “rational” by definition, why is Pi an irrational number?

    • The circumference and the diameter can’t both be rational at the same time. Pi is just the way the two are found to interact, it’s the constant describing their relationship. In other words, there is no fraction that exists to perfectly describe the relationship. The closest is 22/7, but it still goes off at the 3rd decimal. If you have a circle with, say, a diameter of 10, the circumference is always going to be 10*pi, or 31.4159… In the same way, if the circumference is 10, the diameter ends up being 10/pi, or 3.1831… So, at any time, yes, one of them can be rational, but then the other one can’t be. So the ratio between them can also never be rational. :)

  2. Math still hurts.

  3. Love the “cup trick”! ^^

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

Join 616 other followers

%d bloggers like this: