Demystifying the number Pi

As many of you have surely heard, the international Pi-Day is taking place today! But for many it is not clear why there is a Pi Day and what makes Pi so special. For these people I would like to introduce Pi in this post.

Definition

The number pi is defined as the ratio of the circumference of a circle to its diameter and has the value 3.1415926535... This may sound somewhat abstract at first, but can be explained quite simply. You can buy either two 25cm diameter pizzas or one 30cm diameter pizza for the price of $20.

If you now want to know which of the two offers is better, i.e. gives you more pizza to eat, you need the areas of the pizzas. But how do you find the area of a circle? For rectangles the whole thing is very simple. You simply multiply the lengths of the two sides to get the area. For a circle, however, the whole thing is a bit more complicated. And that's where Pi comes in. The area of a circle is calculated using r^2 * pi.

For our example this results in the following areas:

(25cm / 2)^2 * 3.1415 = 490.86 cm²
(30cm / 2)^2 * 3.1415 = 706.84cm²

Through this calculation you easily find out that it is better to buy the two 25cm pizzas instead of one 30cm pizza!

... and now what?

Now you know what pi can be used for, but you probably still think it's funny why such a fuss is made about it.
This has several reasons. On the one hand, Pi is an irrational number, i.e. it has an infinite number of decimal places. This may seem a bit strange, since it originates from something as natural as the circular area. And many people have made a sport of memorizing as many decimal places of Pi as possible. The current world record is 100'000 memorized decimal places and is held by the Japanese Akira Haraguchi.

On the other hand, pi also has an important role in mathematics. Pi occurs in many important formulas and is certainly one of the most important constants of all.
For example, in mathematics one almost always uses the radian measure. A circle has 360 degrees, which corresponds to 2pi. pi/2 then corresponds to 90 degrees and so far.

I hope I was able to demystify some of the mysterious side of Pi with this post. But of course there is much, much more to discover about the number Pi.