MARCH 14 is celebrated all around the world by geeks and nerds as Pi Day because 3-14 are the first three digits of pi.
Pi was first discovered by mathematicians as the ratio between a circle’s circumference and its diameter. It is named after the Greek letter that is first in the Greek word perimitros, which means perimeter.
If you get any circle and divide its length around (its circumference) and its length across (its diameter or what can be thought of as its “width”), you get pi. That’s true for any circle, no matter how big or small. Any circle at all. In fact, this fact is so essential to circles that if the ratio of a shape’s width and its length around is not equal to pi, then that shape is not a circle.
That the ratio between any circle’s diameter and its circumference is always this constant, which can be approximated as 3.14159 to the fifth decimal place, has led people to endow this special number with cosmic, sometimes even mysterious, spiritual, or religious significance.
A moment’s thought would make you appreciate part of the mystery that the ancient mathematicians, philosophers, and mystics have attached to pi. Just think about it: we haven’t gone measuring the circumference and diameter of every single circle all around the world. Such a thing is not possible. And yet if we say that for every single one of them the ratio between the circumference and diameter is the same—3.14159 and so on—we would be saying something true.
In fact, we can say such a thing not just for all circles that exist in the world, we can say it for all possible circles. That is an astounding fact!
There are so many circles that exist in the world. How many? It’s hard to tell, but we know that it’s a ridiculously large number. Still, it is a finite number. On the other hand, there are infinitely many possible circles! For every single one of these infinitely many circles, the ratio between the circumference and diameter is equal to 3.14159 and so on. Give your self a few more moments to let that sink in.
The Pythagoreans, the followers of the Greek mathematician Pythagoras, held mystic beliefs about numbers. They believed that the world is made of numbers, that numbers are the fundamental building blocks of reality. But for many of them, it wasn’t just any numbers, it was whole and natural numbers—0, 1, 2, 3, and so on. They thought that all numbers could also be constructed from natural numbers. For example, 0.5 can be written as ½, the ratio between 1 and 2. Meanwhile, 0.25 can be written as ¼, the ratio between 1 and 4. Even the negative numbers can be written in terms of the negative counterparts of the natural numbers.
Pi baffled the Pythagoreans. They tried to figure out which natural numbers pi was a ratio of. Two of them—22 and 7—are close, but these are only good approximations because 22/7 is not pi. They tried and tried to look for the pair of natural numbers whose ratio will give them pi. They tried ratios of ratios—repeating fractions. It seems they have to keep to taking ratios of ratios forever and ever to get pi. It seems a finite set of natural numbers does not exist that can capture the essence of pi. It seems that pi was beyond reason, contrary to reason. Pi was “irrational.”
The Pythagoreans’ search for the natural numbers whose ratio was pi was, of course, a journey to the end of the rainbow. That is why pi can never be written as a finite set of decimals. The digits of pi will go on and on forever, without repeating or exhibiting a pattern; without rhyme and, if the Pythagoreans are to be believed, without reason.
The ancient Indians computed to about five digits, the ancient Chinese to about seven. In the 14th century, the Indian mathematician Madhava and the European mathematician Gottfried Leibniz independently came up with a formula that can spit out as many digits of pi as desired (or as can be quickly computed). Some NASA engineers said that, for the purposes of sending spacecraft to distant worlds within the Solar System, 15 or 16 digits is sufficient.
We celebrate pi because it is a great starting point to the wonderland of wonders and shapes that is mathematics. So next year, take the time to celebrate pi day by seeing how many digits you can memorize, learning about the history of mathematics, writing a piku (a poem whose stanzas have 3 syllables, then 1, then 4), or maybe just eating some pie.
Pecier Decierdo is resident physicist and astronomer of The Mind Museum.