GLIMPSE: The life of π

There will be no mention of any boy on a spiritual boat ride with a tiger in this text. This article delves into a different Pi, one that is equally – maybe even more – wondrous and thought-provoking than the movie.

π (or Pi), for those who have not encountered it yet, is the ratio of a circumference of a circle to its diameter. In more basic terms, it is the ratio going all around a circle to going through the circle, a ratio that is consistent despite the size of the circle and definitely one of the most famous mathematical constants in the entire world.

The mathematical superstar pi is one of the first numbers to ever gain its own symbol (π) based on the original Greek, and is one of the most memorized numbers in human history. Despite its immense popularity, though, Pi is actually quite possibly one of the most irrational and most randomly sequenced numbers known to man. It is irrational because it is impossible to express it as a ratio of two integers, and is non-terminating as it goes on in an endless sequence without any repeating digits.

The history of the usage of Pi goes back to the ancient Egyptians who meticulously applied the number in determining the measurements and proportions of the Great Pyramids. Constructed some time between 2560 to 2540 BC, the Great Pyramid, with a perimeter approximating 1760 cubits, when divided by its height (about 280 cubits) will approximately equate to 2π.

Many experts believe that these measurements were deliberate, but lack of official records hint that the 2π ratio is a mere coincidence. Nonetheless, though these numbers are all in easy non-perplexing decimal free approximations, it is still a great achievement – or miraculous mathematical coincidence – considering the structure’s construction in a period where such calculations were a near impossibility.

The Greek mathematician Archimedes would be the first to rigorously make a close approximation of Pi; at around 250 BC, he calculated for Pi by means of inscribing a polygon within a circle and circumscribing that circle into another polygon. By continuously adding more sides to the polygons, their perimeters gradually neared but never fully reached Pi; thus, Archimedes was able to conclude that Pi is

223/71 < π < 22/7

after computing the polygons up to 96 sides. This value for Pi became so widespread that it stayed as the accepted value of Pi for more than a thousand years, which is why Pi is also known as the ‘Archimedes’ Constant’. Other widely known mathematicians that attempted to extend the known digits of Pi include Ptolemy, Fibonacci, and Isaac Newton, although their contribution never quite trumped the acclaim of Archimedes’.

In the turn of the 16^th century, the use of infinite series gave rise to calculating for specific digits of Pi rather than the previously utilized approximate range. The earliest known use of the infinite series to solve for Pi was in 1400, as started by the Indian scientist Madhava of Sangamagrama who precisely computed Pi up to 10 decimal places.

306 years later, on the other side of the world, John Machin was able to reach 100 decimal places. In the same year of 1706, William Jones became the first to use the symbol “π” as the symbol representing Pi, but popular use of the symbol was only achieved through the works of the prolific Leonhard Euler in 1748.

Topping all other forays into the constant, in 1949, Levi Smith and John Wrench manually computed Pi up to 1,120 decimal places using only a desk calculator.

In the mid-20^th century, after recognizing the mental strain caused by repetitive iterations, humans used early computers to further expand the known digits Pi. From its mere thousand, the computer was able to track Pi’s digits to the millions’ places.

The ENIAC (Electronic Numerical Integrator and Computer) reached up to 2,037 decimal places in 1949, and over years steadily found more digits until it reached a million digits in 1973.

As of October 17, 2011, Japanese Shigeru Kondo computed Pi up to 10 trillion digits using the Y-cruncher program developed by Alexander Lee; the entire process entailed 371 days of computation and verification of the digits. Even more extreme is the current Guinness world record holder for most digits of Pi memorized, Chao Lu, a chemistry student from China who recited 67,890 digits of Pi which took 24 hours and 4 minutes to finish.

But in all efforts to further define Pi, the further discovery of digits has become more of a competition than an actual curiosity for the its significance or applications in the real world, or a contest of bravado among computer engineers. Cosmologically, 39 digits of Pi are enough for computations, as it is precisely proportional to the size of an atom, giving it grounding in physical, tangible things. Otherwise, being capable of solving more digits of Pi is only an indicator of the power of your computer processor.

Regardless of how abstruse some might make it out to be, Pi is a number applied in many fields. Its uses in geometry, trigonometry, chemistry, statistics and related fields, emphasizing its resonance with human progress.

Hence, Pi day is celebrated every 14^th of March (3/14) – in fact it is a national holiday in the land of the Rationalists, France – and serves as a day to honor the very basic yet complex, and very beautiful mathemtical constant that is π.