Pi Day is celebrated today, 14 March,?round the world. Pi (Greek letter ¦Ð) is the symbol used in mathematics to represent a constant ¡ª the ratio of the circumference of a circle to its diameter ¡ª which is approximately 3.14159.?Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern. While only a handful of digits are needed for typical calculations, Pi's infinite nature makes it a fun challenge to memorize, and to computationally calculate more and more digits.
In this post?Dr. Balkrishna Shetty, former Ambassador of India to Bahrain, Senegal and Sweden, looks back on his life with Pi.
I must confess that I fell in ?love with Mathematics in school when I found that ?1/1 + 1/4 + 1/9 + 1/16 + 1/25 +.. = ?¦Ð2 /6. I noticed not only the simple regularity involved but was also astounded by this link between the positive natural numbers from arithmetic and ?the number ¦Ð that I had encountered in the totally different domain of geometry! What's more, it seemed to me to demonstrate what the power of the mind could do that no amount of calculations could ever do, namely, prove this mathematical equality! To make matters more interesting, I found that 1/1 + 1/16 + 1/ 81 + 1/256 + 1/ 625 +... = ¦Ð4 /90, and, more generally, the infinite sum of even powers of positive natural numbers was always a rational number multiple of the corresponding power of pi! That there was this infinite degree of precision and exquisite harmony among different mathematical propositions and even domains bowled me over!!
Unfortunately, ?the proofs then available for these results were either too long or, as in the case of the general result, ?too difficult for me to understand.
Fortunately, I was struck down with jaundice in class 11, and while recuperating, I was able to construct a short and, above all, a relatively simple proof of both the simplest case and the general result! But ?that uncannily close link between natural numbers and pi continued to intrigue me. It was only when in the Master of Sciences ?course at the Indian Institute of Technology, Kanpur, when I was studying abstract harmonic analysis, based on abstract algebra, general integration and topological spaces, that I found one significant clue: the integers (..., -3,-2, -1, 0, 1,2, 3,...) under addition and the circle group { e^ (ix) } under multiplication are the duals of each other as locally compact abelian topological groups.Finally, it provided me with at least one mathematical reason for those out- of- the- blue relationships, though of course, it is still a mystery to me why it should have been so.
I still love pi and it is my favourite number. My simple proof, for which I won an expensive American slide rule at the NCERT Mathematics Summer School in 1968 when calculators had not flooded the market, now appears in my book, What is Mathematics?