August 18, 2022

# Pi Approach Day – what’s behind the magic?

You might remember pi from your high school math class: it’s something to do with circles, right?

In honor of Pi Approaching Day, let’s refresh our memories and even learn something new about the secrets of pi.

## What is pi?

Imagine a circle – or take a plate or a piece of paper and a pencil, and even a compass if you like, and draw one. The circumference of the circle is the length of the line that runs around the outside of the circle.

The diameter is the length of a line from one side of the circle to the other, passing through the center of the circle. Half the diameter, or the distance from the center of the circle to its edge, is called the radius.

Pi can be defined as the ratio of a circle’s circumference to its diameter, or – to put it another way, circumference/diameter = pi.

The letter pi was probably chosen to represent this number because it relates to the concept of ‘perimeter’, which is the distance around the edge of a shape – the circumference is actually the perimeter of a circle – or ‘periphery’, which also refers to an outer boundary. These words start with P in English and start with pi in Greek.

But how much really It is pi? Well that’s about 3.14.

So why don’t we say pi = 3.14?

well pi is not actually 3.14, or 3.14159, or even 3.14159265358979323846 (that’s pi to the first 20 decimal places). Pi is an irrational number: its decimal representation never ends and never repeats.

Pi has been calculated to trillions of digits, but that’s still not exactly pi. It’s just too much, much good approximation.

Another very useful approximation of pi is a simple fraction: 22/7.

AND That is Where does Pi Approach Day come from – 7/22 looks like 22na of July in day-month date format.

Many people also celebrate Pi Day on March 14th, because 3.14 looks like March 14th.º in the month-day format… but we are Australians and anyway, the Australian winter is a better time to eat pie.

## Why does pi appear in so many places?

So pi is a number that describes the relationship between the diameter of a circle and its circumference – so far so good.

So, unsurprisingly, pi is in many geometry formulas about the area and volume of circles, spheres, and other rounded shapes.

But pi also shows up in all sorts of other places that apparently don’t have much to do with circles. In probability, the square root of two pi is part of the formula for the normal distribution, also known as the bell curve. The Coulomb constant, which describes the force between two electrical charges, is defined as one divided by four pi times epsilon zero (a measure of how much electrical charge empty space can store). Pi also appears in the cosmological constant formula, used by astrophysicists to explain the theorized dark energy that may be driving the expansion of the universe.

And there’s more – pi appears in the mathematics underlying epidemiology, fluid dynamics, and even quantum mechanics.

## Is pi magically at the center of everything?

Many concepts involving pi involve circles or spheres. A physical force or electric field that spreads out uniformly in all directions is actually an invisible sphere.

But pi is also related to all kinds of oscillations and cycles – systems and patterns where things move back and forth within a range of values. Examples include the way a coiled spring stretches and contracts, or how a pendulum in a grandfather clock swings from side to side.

Pi is central to describing the sine wave, an undulating curve that oscillates gracefully between one and negative. And many phenomena in science have a sine wave somewhere, from electrical voltage to sound waves, from seasonal disease cycles to the electromagnetic spectrum, which includes visible light, X-rays, microwaves, and more.

Happy Pi Approach Day – and we hope you’ll join us for a chance to grab a pastry-based circular snack and marvel at this impressive number.  #### Annice

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