Okay, so Pi (or π) a mathematical constant.

It's equal to 3.14, or 3.1415926 or 3.1415926535897932384626433832795 — depending on what kind of calculator you use, although it goes on for much longer.

We use it in calculations in geometry and trigonometry, mainly having to do with circles and ellipses and so forth. By extension, it shows up in the sciences — like physics, astronomy, and meteorology, to name a few examples.

What is pi, really?

Simply enough, pi is the ratio of a circle's circumference to its diameter.

Draw a circle 1 metre across, and its circumference will be pi metres. A circle 1 centimetre across will be pi centimetres around.

The circumference of a circle rolled out flat plots the value of pi. Credit: Wikimedia Commons

Ok, but what makes pi so special?

As the above circle unrolls and its circumference is compared to a ruler laid on the ground, the end of the circle will not fall exactly on one of the ruler's marks. In fact, no matter how close together those marks are, or how small of a space they measure, or how closely we zoom in on the ruler, the end of the circle will never fall exactly on the lines, ever.

Pi is an irrational number. What that means is that no matter what you do, you can't divide one whole number by another whole number and arrive at pi. There are examples that come close (such as 22 ÷ 7 = 3.14285714286), but they only give you an approximation. As it is, the decimal places of pi apparently go on forever, without producing any sort of pattern that we can recognize! To the best of our considerable knowledge of mathematics and the universe so far, we'll probably never know its exact value.

As of 2019, pi was been calculated to over 31 trillion decimal places. In 2021, that record was broken as scientists doubled it to 62 trillion decimal places, and as of 2022, a new record was set, increasing the total digits of pi to 100 trillion!

Even with these incredible computational feats, we still haven't found the end of pi. That's why asking a computer or robot to compute the last digit of pi was such a good trick to use in science fiction stories. If the computer or robot didn't overload in the process, it at least bought the heroes some time to escape.

Perhaps if we were able to look at our universe from the outside, we'd be able to see pi resolve down to a simple, rational number. From here, inside the universe, this mathematical constant holds as an enigma of the cosmos.

Fortunately, the cosmos is forgiving enough that we don't need to know pi to the last digit to produce practical results.

Watch below: The fine people at YouTube's Numberphile show how to calculate pi, using pies.

Pi in weather?

How often do we see pi show up in meteorology? More often than you might think!

While there aren't too many exact circles in weather, whenever you have rotation — convection, turbulence, storms, supercells and tornadoes, extra-tropical cyclones, tropical storms and hurricanes — pi plays a vital role in that motion!

Take the example of the 'Fibonacci Spiral' pattern produced by the storm that passed over the United States and Canada back on March 11, 2019.

The "Golden Spiral" overlaid onto the storm pattern is one where the radius of the spiral increases so that it matches a Fibonacci number sequence. The sizes of the boxes that the spiral curves through are 1x1, 1x1, 2x2, 3x3, 5x5, 8x8, 13x13 and 21x21, and it would continue with 34x34, 55x55, 89x89, 144x144, etc.

The radius at any point along the curve, though, can be found with the equation below,

where phi (φ) is the 'golden ratio' (itself an irrational number equal to 1.6180339887...), theta (θ) is the angle from the origin (in radians), and we can see pi figuring prominently in the exponent of the equation.

Frankly, we just can't get away from pi in weather!

Celebrating a mathematical constant?

Conveniently, the name of this particular mathematical constant happens to be a homonym for a delicious dessert treat — pie! Apple pie, cherry pie, blueberry pie, strawberry-rhubarb pie, and even pizza pie.

Pi pie, courtesy koka_sexton/Flickr

As long as it's round, it will do just fine.

Other special constant days

Do we celebrate any other scientific or mathematical constants? Indeed, we do!

There's Pi Approximation Day, on July 22, since 22/7 is a fraction used to approximate pi (it comes out as exactly 3.14285714286).

Depending on whether you write your dates day first or month first, e-Day is on either on January 27 or February 7. It recognizes Euler's Constant, e, which is approximately 2.71 (but it goes on forever, like pi). Calculating compound interest may be its most famous application.

For the chemists, there's Mole Day. A "mole" is a standard measurement of any substance in chemistry, equal to 6.02 x 10²³ atoms or molecules of that substance. As a result, Mole Day is observed on October 23 (10.23), specifically between 6:02 a.m. and 6:02 p.m.

Then there's Tau Day, on June 28, which celebrates the mathematical and scientific constant tau (τ), which is equal to 2 x pi (2π = 6.28571428571...). Or, pi is equal to one half of tau, depending on which side of the rivalry you're on... and yes, there is a rivalry here!

Why? Because a circle is defined as the set of all points in a plane that are at a given distance from the centre point. In other words, a circle is defined by its radius, not its diameter. Therefore, to compute the circumference of a circle, you measure from the centre to the edge, and then multiply that number by 2π, or τ. So, the argument is that tau is technically a better mathematical constant than pi.

Unfortunately, while tau may be better, mathematically, it does not have a tasty food associated with it.

For more on pi, and to try out some cool uses of it, check out NASA's Pi in the Sky Challenge!