It’s Pi Approximation Day!


You might already be familiar with Pi Day celebrated on the 3rd of March (3/14 in US date format), but did you know about Pi Approximation Day?

Held on the 22nd of July every year (22/7), Pi Approximation Day is another chance for everyone to celebrate the most famous irrational number!

This date works because the fraction

is a close (but not exact!) approximation of pi. 22/7 can be used on calculators that don’t have a function, or when an ‘exact’ value of pi isn’t necessary.

So how exact are we talking?

The value of (to 10 decimal places) is 3.1415926536…

The value of 22/(to 10 decimal places) is 3.1428571429…

So, you can see that theses numbers differ from the third decimal place onwards, it’s not perfect. This doesn’t come as a surprise though, as an irrational number by definition cannot be represented as a simple fraction.

However, 22/7 has been in use since antiquity. Archimedes is the first known user of this fraction, when he demonstrated that 22/7> π >223/71. He worked this out using the perimeters of polygons (with up to 96-sides!). This geometric technique allowed him to approach the true value of , but he was only ever able to give a range of values as seen above.

The rest of the history of pi, from then to now, is a story of mathematicians trying to calculate more and more digits. In the 1400s, ‘infinite series’ calculations were developed in India that allowed a greater level of precision than ever before, up to 11 digits. This development rekindled interest in this area and many more mathematicians started their own work, Issac Newton himself was able to calculate 15 digits in the course of his work.

Then, with the development of computing technology in the 20th Century, machines could do the heavy lifting required to reach even loftier numbers of digits. A desk calculator was used to calculate 1120 digits in 1949, and soon after that one of the first general purpose electric computers (ENIAC) managed to calculate 2037 digits (it took over 70 hours though!).

Since then, there have been many developments, and huge amounts of computing power dedicated to calculating quadrillions of digits of pi, testing some of the biggest supercomputers in existence. The current record for the most consecutive digits of pi is over 22 trillion! The file containing that number is over 9 terabytes!

For a visual of what a number of this size looks like, this video shows what a mile of pi looks like when typed out..

For a more practical approach, pi can be estimated by throwing sticks at the ground! Check out this great video with a simple demonstration of a practical take on the ‘Buffon’s Needle’ problem for approximating pi.

But why?

This great video from Numberphile talks about why 39 digits of pi is probably enough for most calculations, as that will allow you to calculate the size of the universe with an accuracy of one atom!

So, why do we do it? Sometimes it seems to just be to ‘break the record’, but doing these sorts of calculations can be used to test supercomputers as well, so it’s not totally pointless!


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