Pi (π) is a real number of special significance in Mathematics. The number π is ubiquitous across mathematics and is a universal constant. In fact, it would be an understatement to call it “universal,” because it exists in any conceivable universe. Pi’s ubiquity extends beyond math such as the spiral of the DNA double helix, the disk of the sun, the pupil of the eye, the concentric rings that travel outward from splashes in ponds. Pi is also extensively used in physics to describe waves and ripples of light and sound and the periodic phenomena such as the alternating electric currents, motion of pendulums and the vibration of strings. It appears in the Heisenberg’s uncertainty equation that defines how precisely we can know the state of the universe. It existed even prior to the Big Bang. It is eternal and unchanging. No number is as famous as pi. The value of pi lies between 3 and 4 but not as a terminating fraction. π (pi) is irrational, non terminating and keeps going forever. While it is true that there are an infinite number of both rational and irrational numbers, we should know that, in a particular mathematical sense, there are way more irrational numbers than rational. Rationals are countably infinite but the Irrationals are uncountably infinite which means that one cannot even assign an order among them. In this sense, there are more irrational numbers that rational. Surprisingly this is also true about people around us. According to Nietzsche, the irrationality of a thing is no argument against its existence, rather a condition of it. Most of what we do is irrational and then we spend a little rational thought in justifying our irrationality.
Even the most analytical thinkers are predictably irrational; the really smart ones acknowledge and address their irrationalities. Einstein says, I never made one of my discoveries through the process of rational thinking. The star of today’s irrationality show is π (pi). Since 3, 1 and 4 are the first three significant digits of π, March 14 (3/14) is celebrated as Pi Day across the world by mathematics lovers. The day was founded by physicist Larry Shaw in 1988, and since it also happens to be the birthday of Albert Einstein, it was a perfect pi-incidence. π (pi) is the ratio of a circle’s circumference to its diameter. The name was coined from the first letter of the Greek word perimetros, meaning circumference. The circle is often the first shape we learn in childhood, and it is come across in nature, throughout, whether in pinecones, rainbows or the cornea in our eye. The circle is everywhere! The first calculation of pi was done by Archimedes of Syracuse (287-212) who was a Greek mathematician and astronomer. He calculated the area of a circle by using the Pythagorean Theorem. The magic of Pi is used every day and everywhere be it engineering, construction, Global Positioning System, simulations, radio and television, telephones, power generation or mechanical motors. Pi crops up even in places that have no ostensible connection to circles. Some historians also believe that pi would also have been used during the construction of ancient Pyramids of Giza because the structures are nearly perfect geometrically. Pi has been used by different cultures throughout history. While calculating the area of a circle, the ancient Babylonians and Egyptians used approximations for pi. Zu Chongzhi, a Chinese mathematician who lived between (429 and 501), created his own ratio that approximated pi in much the same way as Archimedes did. Similarly, Georges-Louis Leclerc (1707-1788), a French mathematician, showed that Pi could be calculated with probability. Another mathematician namely David Chudnovsky built his own supercomputer with his brother to explore the inner infinity of pi. He sums up the power of pi rather eloquently: “Introduce your students to the vocabulary of circles—center, diameter, radius, circumference, arc, chord, tangent, and pi with this math talk-rich lesson for Pi Day on measuring circles.” Pi has been calculated to over one trillion digits beyond its decimal point. On account of being an irrational and transcendental number, π (pi) continues infinitely without repetition or pattern. It keeps going forever. Over the ensuing centuries, Indian, Chinese and Arab mathematicians have further extended the number of decimal places in π (pi) through tedious calculations. However, by the end of the 17th century, new methods of mathematical analysis evolved in Europe to provide improved ways of calculating pi involving infinite series. As for instance, Sir Isaac Newton used his binomial theorem to calculate π (pi) upto 16 decimal places. Similarly, in the early 20th century, the Indian mathematician Srinivasa Ramanujan developed certain exceptionally efficient ways of calculating pi which were later incorporated into computer algorithms as well. The typical calculations need only the first few digits but because of an infinite nature, π (pi) is a fun challenge to memorize, and it requires computations to calculate more and more of its digits. The teachers, scientists and mathematicians hope that the holiday will help increase interest in math and science across the world, through museum exhibition and instruction, pie-eating (or throwing) contests and much more. It is a day to satisfy the left-brained and the sweet-tooth and keep them inclined. How will you be celebrating?
Dr. Qudsia Gani is Assistant Professor, Department of Physics, Cluster University Srinagar