# How Many Digits of Pi Do We Really Need?

It was pi day last month, and call me an idiot for not releasing this video then, but I’m
just not a math nerd.
I’m an engineer and all this hype for a mathematical constant goes a little over my
Internet drama has been born out of people for and against pi.
A quick search of YouTube will yield 10s, literally 10s of videos, teaching you how
to memorize the digits of pi.
The Guinness World Record for reciting pi with the most digits has changed hands multiple
times with the current champion, Rajveer Meena of India, managing 70,000 digits in 10 hours.
Fair play Rajveer, fair play.
Now go use that brain for something actually useful.
Jokes aside, this is a genuinely impressive act of memory.
Pi is a fascinating mathematical constant, that defies any tricks for memorisation.
It just keeps going and going and going.
It’s infinite and it doesn’t repeat itself.
You just have to brute force memorise it.
And while these lads are spending days learning as many digits off as possible, mathematicians
are working away at calculating the new longest string of digits.
Pi is found fairly simply by dividing a circle’s circumference by its diameter.
So the diameter of a circle can fit into its circumference 3.14159 26535 89793 23846 26433
83279 50288 4197…..
Okay, so you get the point, that is simple on paper, but in practice it is far more difficult.
Measuring a circle's circumference accurately is practically impossible.
Even your best attempts with a measuring tape will be off by the thickness of the measuring
tape.
Archimedes was the first to calculate pi with any level of accuracy with an ingenious method
called the “method of exhaustion”, and yes it was nearly as exhausting as this video’s
attempts at snarky humour.
He started estimating pi with squares, which sounds unconventional, but it makes a lot
of sense.
In the mind of archimedes a circle was simply a polygon with an infinite number of sides,
so by starting with a polygon with fewer sides we can get a very rough estimate of pi by
calculating it’s ratio of circumference to diameter.
Let’s start by placing a square inside of a circle with its corners touching the circles
sides.
We can then find the ratio of this low estimate of pi by dividing the sum of the squares sides
by its diagonal diameter, which in this case is (4/root 2): 2.828 This is our lowest estimate
of pi.
Now let’s place a square with it’s side touching the circles side, and this time we
will divide the sum of the squares sides by the length of one of the squares sides, which
gives us 4, the number of sides a square has.
In boths of these cases we are dividing by the circles diameter, that figure is accurate.
What we are lacking in accuracy is the measurement of the circumference.
The inside squares perimeter is too small, and the outside squares perimeter is too big,
but now we know pi lies between these two numbers.
Now we just need to narrow it down, and we can do that by increasing the number of sides
of the polygon.
Each time we add a side those two figures will get more accurate, and eventually the
two numbers will start overlapping in their digits.
This is how we got our first known digits of pi.
This continued on for a couple of centuries, with mathematicians out exhausting each other
until eventually someone started using computers and now we are just exhausting them.
We now have 2.7 trillion digits of pi calculated[2], and for some reason through these millenia,
an engineer never stood up and yelled:
“shtop.
For the love of all that is holy stop.
We have enough digits.
We don’t need any more.
We don’t have any circles big enough to justify this level of accuracy, go to bed
ye lunatics.
~deep breath~"
Because in the end of the day, that’s what pi is used for.
It’s for calculating the circumference and area of circles.
It’s for converting degrees to radians, and this is where the arts of mathematics
and engineering differ.
While mathematicians obsess over accuracy to the trillionth digit, engineers aim for
“good enough”, and good enough turns out to be 3.141592653589793 for the people that
work with the biggest circles.
NASA.
Let’s take the distance to Voyager 1, which is currently about 21.7 billion (21690753480.975746)
kilometres away in interstellar space, as our radius.
Say we want to calculate the circumference of a circle with a radius this large.
What difference would adding one extra digit of pi provide?
That’s the difference between 15 decimal places and 16 decimal places.
This is actually tough enough to calculate with a calculator or excel as both are limited
in the number of decimal places they can calculate.
So using this online high precision calculator we can find that the circumference of this
circle will be about 136 billion kilometres, and if we use on extra digit it will be 8.67
millimeters closer to the actual value.
That’s tiny and we just travelled out of the solar system.
That’s why JPL and NASA don’t need any more figures and the chances are you don’t
need anymore that 3.1416.
So I’m gonna be the engineer that yells shtap.
We have better things to be worrying about, pi is literally infinite and we are never
going to reach the end.
What is the point.
If you don’t want to waste your life completing pointless challenges.
You could try the challenges on Brilliant instead.
Where they present you with daily challenges that you can solve with Brilliant’s community.
Brilliant just released offline courses on iOS, so you can work on learning new things
even on an underground train or a plane.
Brilliant also recently released their fantastic course on Python coding called Programming
with Python.
Python is one of the most widely used programming languages, and it is an excellent first language
for new programmers.
It can be used for everything from video games to data visualization to machine learning.
I used it in my own Master’s thesis to create custom plug-ins for my finite element analysis
software, but I had to teach it to myself and work through consent errors.
This course will show you how to use Python to create intricate drawings, coded messages
and beautiful data plots, while teaching you some essential core programming concepts.
This is just one of many courses on Brilliant, with more courses due to released soon on
things like automotive engineering.
If I have inspired you and you want to educate yourself, then go to brilliant.org/RealEngineering