What is Pi?

Pi is a number that everyone has heard of. It is a staple of our maths education from a fairly early age. Some may recall it is approximately 3.14. That funny looking symbol, π is engraved in our minds, but what actually is it? What are the practical uses for it? And what on earth is an 'irrational number'?

Let's be curious and ask, 'what is pi?'

Circles

Pi-Day is celebrated on the 14 May (3/14 in US date format) or
22 July (22/7 in UK date format - approx 3.14)
"Pi pumpkin pie, January 2008" by Paul Smith
originally posted to Flickr as Pi pie.
Licensed under CC BY 2.0 via Wikimedia Commons.

Whenever pi is mentioned, food is the first thing that pops into most people's heads. For mathematicians it is the circle that pops up. Most people are aware of a connection between pi and circles. Many will be able to recall that $area=\pi r^2$, or that $circumference={2} \pi r$. But what does that pi actually mean?

Pi is a ratio, that is a relationship between two numbers, of the circumference of a circle and its diameter. If you divide the circumference by the diameter you will get $\frac{\text{C}}{\text{D}}=\pi$. In fact you can rearrange the equation for the circumference to give you that if you remember that the diameter D is the same as two radii.

The value of that ratio is always the same. No matter the size of your circle, C over D will always equal 3.14159...

Irrationality

An irrational number is not a number that is impossible to beat in an argument. An irrational number is one that cannot be expressed as a ratio between two integers (whole numbers). Irrational numbers are infinite. That doesn't mean they are really big, but that there is no end to the number of digits in that number. 3.14159 is just pi to 6 significant figures. It is an approximation. Currently, we know pi to over 12 trillion digits. That is a lot of digits! A trillion is a thousand billion. It took the team 92 days to compute those digits (it previously took them over a year to calculate 10 trillion digits).

Another feature of irrational numbers is that they are non-repeating. In other words it will never loop back the beginning and keep repeating the same set of numbers. For example 1/3 is equal to 0.333... . The 3 keeps repeating infinitely. In pi, the sequence never restarts.

So, as a consequence of being infinitely long and non-repeating, pi contains many strings of seemingly significant digits. In fact my home phone number (7 digits long, without the area code) occurs 17 times in the first 200 million digits of pi. Scientists are fairly sure that each digit 0-9 has an equal chance of occuring at any one point, so that technically means if you were to convert pi's digits into ASCII code (text) then the name of every single person you will ever meet will appear in order at some point in pi's sequence. Of course we can't work out all the digits (physically impossible) so we will never be able to empirically test this theory, but it's still pretty cool! You can search the first 200 million digits of pi at this website.

Practical Applications

Whenever anything related to maths or science is mentioned, there will typically be someone who asks 'what's the point?' I went some way to answering this in Why Bother With Science?, but I can be more specific here with regards to pi.

The most obvious use is that pi is required to work out the area or circumference of circles. We can all remember the worksheets where you had to work out the amount of wood needed to make a circular fence or something. They are actually problems we may face in real life, so pi is useful there. But where else?

"International Space Station after undocking of STS-132" by NASA/Crew of STS-132
http://spaceflight.nasa.gov/gallery/images/shuttle/sts-132/hires/s132e012208.jpg
(http://spaceflight.nasa.gov/gallery/images/shuttle/sts-132/html/s132e012208.html)
Licensed under Public domain via Wikimedia Commons.

NASA uses pi to 15 or 16 decimal places to do calculations to keep their spacecraft in orbit and stable. But maybe you want something more applicable to you. Think for a moment about the Earth. It is spherical (well, almost). If you travel 1 metre in a straight line you would be travelling straight. However if you are a pilot flying a plane from one country to another in a straight line, you'll actually be travelling along a curve due to the Earth's curvature. The calculations required to make a plane travel straight involve circles and pi.

Pi is also used for measuring angles in radians (rad). We are used to angles in degrees, but radians are often used in science. 360' is the same as 2π rad. This system works its way into trigonometric graphs (sine and cosine waves). Those in turn are vital for radio, TV, phones, etc...

For most people the only time they will personally use pi is for working out areas and circumferences, but having an understanding that pi is used in many areas is important. And this blog is all about being curious, so I urge you to look up some more applications of pi or investigate one of the ones above a bit further.

What Pi sounds like

In the comments section, Amanda Wilcox shared this video:

Curious Fact

The world record for reciting the digits of pi is held by Chao Lu. On 20 November 2005, Chao recited 67,890 digits of pi over 24 hours and 4 minutes. (guinnessworldrecords.com)

Do you have fond memories of pi from school? Did you find any interesting strings of numbers in the first 200M digits of pi? How many digits can you recite pi to? Let me know, along with anything else on the subject, in the comments below. As always you can share (please do!) this article using the buttons on the left and underneath, and you can follow It Is All Science with the links on the right.

Remember, it is all science. So let's be curious!