The beauty of Pi

On Pi Day, March 14 – a date that coincides with Pi’s best known value of 3.14 – I asked grade eight children what they knew of Pi. They responded by reciting formulas. But they knew nothing more. They neither knew about the fascinating origins of zero in our Subcontinent nor about famous mathematical events, such the measurement of the Earth’s circumference by Al Beruni near Pind Dadan Khan.

Teachers say that, aside from what is in textbooks, children in our schools, even in private ones, generally have poor knowledge of the mathematical world. Our own mathematicians are unknown to them, even world famous ancient mathematicians of the Subcontinent, like Aryabhata or Brahmagupta. This is lamentable. No wonder that Pi Day passed unnoticed in our country.

Mathematics must be popularised. History is evidence that no country advances economically or otherwise without a mastery over mathematics. Celebrating Pi Day nationally each year would be a small but significant step to start popularising mathematics. America has been celebrating Pi Day since 2009 to encourage ‘schools and educators to observe the day with appropriate activities that teach students about Pi and engage them about the study of mathematics.’ We should do the same.

Pi is a fascinating number to begin this effort and would certainly catch the imagination of our children. It is a celebrity among so many interesting numbers like Phi, which represents the golden ratio and has been used in art and design for over two thousand years; and e, i, 0 and 1, which are no less important and interesting.

Pi has a fascinating history. It has been studied in every millennium and in every culture. It is examined today as seriously as in the times of Archimedes of Syracuse over two thousand years ago. The urge to understand Pi and calculate it ever more accurately has challenged people since ancient times. Usually associated with circles, Pi also turns up in places that have nothing to do with circles.

Circles are common in nature. We see them in flowers, in our eyes and in the cross-section of an egg; and in the shapes of the moon and the sun. Because circles are so common in nature, they were recognised eons ago. But the proper calculation of Pi started only 4,000 years ago, dictated primarily by the practical needs of water management, engineering, construction and astronomy. The Babylonians imputed the value of Pi by calculating the area of a circle as three times its diameter. Around the same time, the Egyptians inscribed an improved value of Pi on the famous Rhind Papyrus, dated 1650 BC. Ancient Hebrews, too, were happy with a value of Pi of three, which served them well in all their uses.

A thousand years later, the calculation of Pi took a major analytic turn thanks to Archimedes, the greatest mathematician of the ancient world. He calculated the value of Pi from mathematical principles instead of directly measuring and comparing the circumference and diameter of circles. He found the limits of numbers within which Pi must lie by calculating the area of polygons that inscribe and circumscribe the circle. Archimedes’ method of calculating Pi was not improved upon for another 2000 years.

In the sixth century, near River Indus, the great mathematician Aryabhata calculated a similar value of Pi. He lyrically expressed his discovery in a poem called ‘Ganita’, like he did his other discoveries. Aryabhata also measured the Earth’s circumference and celestial distances. As in Greece, his calculations of Pi were prompted less by practical needs and more by abstract geometric concerns. Aryabhata used positional, decimal-based arithmetic, making calculations easy. His arithmetic is still used today.

This ‘modern’ arithmetic arrived in Europe via the Arabs half a century after Aryabhata. It was still not fully adopted for another half a century because of resistance by clerics who called it ‘diabolical’ because they suspected that it was Islamic. A similar resistance to mathematics in India, spearheaded by Ahmed Sirhindi, called mathematicians “Idiots... because mathematics and its learning could not be of any use in the salvation of men in the life hereafter.” Following Ahmed Sirhindi, the Muslims of the Subcontinent stepped out of the onward march of mathematics, science and technology. And remain largely in the stranglehold of irrationality and unreason.

Meanwhile in the West, countless mathematicians of the seventeenth and eighteenth centuries were prey to the fascinations of Pi. Geniuses, like James Gregory, Gottfried Leibniz, Leonhard Euler used Calculus and innovative ways to express Pi in equations and calculated Pi to unprecedented digits. Euler popularised the Greek notation of Pi and produced much of modern mathematical nomenclature.

The present record, as of November 2016, calculates Pi to over 22 trillion digits. Present methods use spectacular series and iterations based largely on the work of Ramanujan, another brilliant mathematician of the Subcontinent. Yet, the exact value of Pi remains elusive and so does the riddle hidden in the simple ratio of any circle’s circumference to its diameter.

For all practical purposes, including for engineering and architecture, and even for celestial calculations, a value of Pi with ten digits suffices. This would calculate the circumference of the earth correctly to the fraction of a centimetre. Forty digits of Pi would give an accurate estimate of the circumference of the Milky Way. So what could possibly be the motivation of calculating Pi to endless digits? Because, as David Blatner explains in his book ‘The Joy of Pi’, “The search for Pi is deeply rooted in the human spirit of exploration – of both our minds and our world – and in our irrepressible drive to test our limits.’

Pi’s mystique is, therefore, less in calculating more digits and more in the complex, irrational manner it unfolds. Its digits do not repeat. It is impossible to guess the following digit. It is infinite and infinitely intriguing. It is found in all subjects, including physics, architecture, statistics and even biology and the arts. Pi also appears in the equations of the Theory of General Relativity of Einstein, whose birthday also falls on Pi Day.

Pi has engaged and intrigued many of the greatest mathematicians. It has been an integral part of the mathematical culture for several millennia. Celebrating Pi is therefore also celebrating mathematics, which Bertrand Russell says “possesses not only truth but supreme beauty – a beauty cold and austere, like that of sculpture, yet sublimely pure and capable of perfection such as only the greatest art possesses.”

Aside from searching for the truth and creating beauty, mathematics paves the way for scientific advancement. Popularising mathematics means promoting reason and the quest for beauty and truth as a guiding principle of our society; It means finally getting out of the stranglehold of present-day clerics who still echo the dogmas of sixteenth-century bigots.

The writer is a freelance contributor.

Email: khwaja.sarmad@gmail.com